First accurate read of their dynamic I've seen in a long time, so thank you people! <3
But I wanted to add (long ass post incoming, i'm so sorry in advance), Knock Out is a very personable or spiteful bot depending on how others treat him. He can handout genuine compliments as easily as he can hand out insults. But he cares a great deal about mutual respect which is why he goes out of his way to try have a positive relationship with the other cons even though it backfires a lot or he gets punished or hurt in retaliation (often out of nowhere but that's notably from Starscream but Screamer is an abusive POS and Megatron has a 'might makes right' mentality). Equally, KO is also very much a tit for tat kind of bot so he will retaliate when you are hurt him or wrong him (god forbid it's Breakdown someone hurts). But like OP stated, he never lashes out at Breakdown because he knows BD well enough to know it's an accident and he would never do that intentionally. Also BD probably makes up for it by fixing it.
On the topic of his relationship with Breakdown. Their dynamic is incredibly healthy and forged on mutual respect and trust, and on communication. They have clearly known each other and been friends for a very long time to have been able to work through their differences and forged the bond they have now. (notably, despite their obvious differences, they also have a lot in common and as far as they're concerned, they're the funniest bots in the world, hence why they're the only ones that get their humor. They probably both have equally terrible pasts too just in the different contexts of their own cast but this is just me theorizing at this point.)
When KO disappears unannounced to go racing, BD is the one who not only asks him where he is, but also tips him off that Screamer is looking for him and and he's in trouble. There's no animosity in BD's voice or words, it's just quiet friendly exasperation of someone who knows their friends antics far to well, and it lasts only so long a he's explaining that Screamer is involved, but he then asks with genuine curiosity where KO actually is.
Later in the same episode, KO runs off again, but actually notifies Breakdown, having remembered the earlier call and that BD worries about where he is. (KO is not a soldier mind you, which means he's more likely to bail on the fight which BD 100% understands and respects and will follow along with it if necessary. In one of the prime comics, it's BD that tells KO they need to go because KO is stuck in freeze response trying to understand where things went wrong with his invention.) They also regularly check on each other while in the battlefield. (please note where ko is standing after BD loose his optic when they are on and off the battlefield and think about the context of what is going on in the moment.)
Let's not forget that it's Knock Out himself that says that Breakdown acts like the big mean brute, but he actually isn't, telling us that Breakdown takes care of his finish for him. (note that KO is noticeably less explosive about his finish once it is 100% confirmed to him that BD is dead, suggesting part of the value he holds about his finish, is the fact that BD is the one that cares for it.)
Also, BD helps him in the medbay as a nurse, taking care of KO's patients when he's away. Breakdown is a lot more intelligent than people believe (both in the show and in the community). He defo wasn't educated like a high class bot would have been but schooling is not a mark of someone's intelligence and what medical skills BD does have, were mostly likely taught to him by KO, who trusts him to take care of his patients while he's gone, and if something does happen, KO is literally a call and a bridge away and can come back when needed. (this happens IRL too, it's the nurses that take care of the patients every day care, not the doctors) They both also worry and are concerned for the vehicons in different ways, BD more so that KO, but KO is more of a social chameleon than BD and is also able to emotionally detach himself from situations if necessary. (he's a doctor and a surgeon after all, needs to be able to compartmentalize to do his job effectively - Something we see him do a fair bit in the show actually but his face gives away his true feelings on the matter, at least until he slips the mask back on.)
KO's shift in character after he learns of Breakdowns death is for three reasons:
1- he's in survival mode. Fear is running the shop and influencing his logic. He doesn't have someone he trusts at his back anymore and the reality of just how vulnerable he is without him sets in. Leading KO to double down on proving to Megatron that he doesn't in fact need Breakdown with him to be useful to their cause, he is valuable alone even without Breakdowns strength besides him, AKA trying to increase his own odds of survival in the toxic dynamic of the cons. TLDR, he's in a fawn mode towards Megatron because that increases his odds of NOT being killed off. (which is also why he attaches himself to Screamer later. Screamer got pardoned, aka is valuable, by being with Screamer maybe KO can be seen as equally as irreplaceable - It's not because he likes Stascream because he doesn't, he detests Screamer but is being polite about it which is why his compliment to him later comes across as awkward, it's not a genuine compliment - something KO usually does without effort and does so freely, handing out genuine compliments is just a display of his own inner confidence - this is about calculated survival)
2- KO wants out of the Cons as early as mid season 2. After learning about what the omega keys do, and being trapped in the wall and unfairly punished by Megatron for something that ultimately out of his control and Megs did nothing to help prevent because it was 100% preventable had he take 2 mins to ask for guards or back up, KO starts looking for a way out, that's when survival mode truly kicks in. (Megs has a bad habit of setting his non-favored underlings up for failure and then blames them for it... He was more concerned about the possibility of KO loosing the key than actually doing something about preventing Smoke escaping and the key being swiped right from his own hand, and thus it was lost through his own negligence and he STILL blamed KO for it.)
3- KO is silently grieving. Grief doesn't always look like screaming or crying or even anger (Anger is something we do see in him actually, he takes it out on the autbots a lot but he's keeping it in fairly well.) Very often it can looks like someone going quiet, retreating into themselves and just going through the motions of life. (especially so if they have a history of trauma or abuse) Aka suppressing it because it doesn't feel safe to show those other feelings. And in the context of where KO is at in the show at that point, it 100% NOT SAFE for him to show his feelings. So he puts on the mask and gets back to work because that's what Megatron demands, but there's this undercurrent sense of resentment and detachment in how KO behaves after that point towards all the cons. He's tired and wants out. That doesn't mean however the rest of the grieving process won't happen later once he's safe then the rest of the feelings might surface for him to process later, but again it could look very different from the stereotype , textbook definition of what it's 'supposed' to be like. Life is not black and white like that and neither should characters be.
(Sorry these are from youtube so the resolution is ass but -) Look at this face! Dx We see the sadness in him before he swallows his emotions back and goes back to the whole 'evil doctor' shtick, aka perform the act, the role that Megatron expects. There's a non-verbal communication that follows between himself and Silas, that whatever follows is personal, this is about revenge. "eye for an eye" hence why he taps that stolen optic. Silas immediately understands the gesture, the intention and meaning behind it. Ko is using a human analogy to make himself understood in a non-verbal way because he can't say it out loud on the Nemesis and omfg bravo animators! (I should also add, cybertronians place far less importance of the materialisticness of their bodies since they can easily replace and fix things, unlike us - Their spark is what really matters to them since it contains everything that they are on a personal and spiritual level, making KO a peculiarity in some cases - Also Starscream's comment about Ko's feelings on the matter of him experimenting with Breakdown's body was rude as hell and even KO himself had a moment of disgust and anger in his face at the question before falling back into his role. )
The animators were very good at micro expressions and body language. There's so much context added to the dynamics of the characters hidden away in glances, small expressions, subtext and blink and you miss it moments. And on a single watch through, they're all very easy to miss and give a totally different view on the chars. (Fanon defo doesn't help with these images.) So if you care about accurately representing the characters for who they canonically are, (no harm in headcanons so long as they're actually informed on the original material, i have a list as long as my arm too- don't worry) please, i beg you, watch the show again and analyze it. Listen to the subtext and non verbal communication because they are very common and tell you way more than what the chars actually tell you because there's unreliable narrators. :) Prime's spotty and sometimes questionable writing aside, "show, don't tell." is a fundamental core of story telling and is very prevalent in the show.
Anyway that's enough of my ramble (thank you if you made it this far and i do apologies ^^;), I could go on and on about how healthy their dynamic actually is and the depth of their personalities and theorize endlessly about their past and what made them this way and how their friendship became a thing. They are genuinely complex characters with their own morals and beliefs but playing the role of evil henchman, and their friendship is defo an outlier in the context of the show and arguably a lot more realistic.
Knock Out and Breakdown deeply care about each other and have a very strong, genuine, healthy friendship and bond regardless of whether it's only platonic as in the show or even romantic as the fandom prefers. (and was retroactively confirmed) They're just more realistically quiet about it, living life in the moment, because ultimately, in universe, their friendship and their lives with each other is nobody else's business. Their companionship and dynamic matters to them more than other peoples opinions of them and that's lovely to see :).