I see why ur the CEO of PulseDragon DANG ur good at this. What drew you to the pair in the first place?
Returning to the top now that I've typed this out it's honestly a bit wordy so apologies in advance =0= 🎶 thank you for asking btw I like talking about them
Since inception (and I've been a fan producing Han76 content since OW1 release, though those accounts I posted it on no longer exist), I've always felt that the two of them are ultimately two sides of the same coin.
A lot of the very early lore simply casted them both as very jaded, tired, angry, and lost. I felt that perhaps it would not ever be realistic for them to completely be free of that (within the narrative), but that they would benefit from having someone to be lost with. Alone together is better than alone apart.
Over time, and as lore has been expanded upon and elaborated, a lot of parallels have continued to be drawn between the two of them: both totally out of their depth, neither loving or craving the violence of their lives, operating out of a type of perceived duty that they MUST fulfill rather than any personal desires to be in the fight (think Lucio to some extent, where the fighting and the valor and the helping people is the beginning and the end).
We know more now about how Jack never really wanted to be Strike Commander (Bastet) and how much of his continued presence and elevation (much to his own detriment) within the Overwatch organization had more to do with his looks and pleasant personality than any desire he had to stay (Valkyrie, Bastet, Declassified). We know that he wanted a family (Bastet) and that he's TIRED and lost. He joined the military early in his life and that basically ripped any dream of him ever being normal away, even if he didn't know until decades later.
Hanzo is much the same. Ultimately his decisions are his own but he is a victim of circumstance like Genji was (hence why Genji forgives him now, beyond his own journey for inner peace). We also know that he craves a normal life, and he alludes to settling down soon (voicelines). Much like Jack, his continued presence in the narrative is led by regret rather than any interest in fighting (Where Honor Lives, voicelines, and the Dragons cinematic). I would like to think that healing would be possible for both of them to some degree; and I believe that they could be good for each other. They both do ultimately crave normalcy and love.
They contrast a bit as well in a way I think is nice, with it being understood to some extent that Hanzo is actually a bit shy (not in the commonly presented way where he's a quivering waif, but rather that he simply clearly does not have a lot of experience dealing with people on a purely personal level for a 40 year old man), whereas Jack commands a bit more attention (essentially a retired politician). I think that this adds good layers to how they can interact.
On a purely aesthetic level they tend to work as well, both have a distinct blue theming that makes them pleasant to see together. Their silhouettes look very nice together, and they carry themselves (in terms of stance) in a very similar way.
Nowhere else to put it but it also amuses me to no end that they have a similar sense of humor. I think they would make each other laugh.