How do you imagine Claude x Felix would look like?
I can only imagine Claude and Felix as toxic and one-sided. Or rather, I prefer to interpret their relationship that way. Claude was always his prince before he was his friend (in my opinion). I don't think Felix could ever perceive him as a potential romantic partner on his own. It wouldn't be real love, it would be a kind of idolatry.
If he'd have feelings for Claude, he would choose to love him silently, chastely, which even if that love was secretly reciprocated, would most likely result in Claude not revealing his own feelings because he would not want to be seen as a loser in love again. They would be stuck in a stalemate where each of them would believe their feelings were unrequited and they'd keep them secret from one another. Neither of them would be willing to make the first step. Felix because of his duty, Claude because of his pride. I can't imagine Felix doing anything other than punishing himself for his feelings if they'd ever went into the romantic/sexual direction. (if he believed they were unwanted on Claude's side)
It could also be possible that Claude at some point has enough and just takes what he wants. That he forces Felix more or less into a relationship and takes advantage of the fact that Felix can't say no and is so loyal that he would really do anything for Claude. That would mean that Felix doesn't think very highly of himself and sees himself only as a tool with the only task to serve Claude and fullfill his every need. That would include sexual pleasure too. I think the problem in their relationship is that Claude's personality is very dominating while Felix has a tendency to back down, can't set boundaries and has a hard time rejecting him because of their status difference. For him, Claude's wish would be his command.
I also wonder if this is why Felix has trouble recognizing Claude's tyrannical behavior and is unable to take counter measures against them, since his mother may have taught him from an early age that he has to put Claude above anything and he must learn to ignore his own needs when they come in conflict with Claude's will. Or it was the other way around, the early death of his mother prevented him from ever being taught to take his own wishes into consideration and realize that his master is not always in the right no matter how much he adores him.
I imagine that Claude's and Felix' relationship was a strong friendship at first (the novel describes them as bosom brothers I believe), perhaps I allow myself to imagine that Claude had an innocent puppy crush on him (or vica versa) because I hc that young Claude fell easily for people who showed him kindness and never acted on his feelings because he wasn't aware of them or didn't want to ruin their friendship and he was content with what he had, but when they got older Claude began to demand more and more from Felix the more he lost. Basically, Felix had to give him the love that Claude was meant to receive from his mother, Anastacius, Penelope, Diana and so on. Claude demanded an enormous amount of love and attention from a single person, since he himself gave up on forming an intimate bond with others after the negative experience he had with the people he let into his heart so easily. Realistically that one-sided relationship of giving and taking would eventually end up being very draining on Felix and wear him down. But Felix wouldn't be able to recover from it and put space between them because it would just trigger Claude's abandonment issues. He'd get even more possessive and would view any positive relationship Felix might form with others as a threat that needs to be removed. I think young Claude would have been anxious that they'd grow apart and wouldn't like the idea of Felix making experiences that he doesn't/meeting people that he doesn't know/going to places that are foreign to him for a longer time. And that's why they are almost always together. I just can't see it ending well. For manhwa Felix who's entire being revolves around making Claude happy perhaps, but not for a Felix who would have acted like an actual person. Claude values Felix the most but at the same time he has no problems to insult him casually and canonically tell him to shut up or else he "kills him" for protesting against something immoral.
I also like to imagine that there is an element of self projection to their relationship. My headcanon is that just like Claude, Felix was an illegitimate child of a commoner (his mother was a maid) and a noble (his father was the duke). Both of them lost their mothers when they were young and were raised together. Claude might have difficulties understanding that Felix doesn't want the same things as him just because they were raised the same and had similar experiences and share the trauma of losing a parent. He might decide over Felix' head matters that concern him without consulting him first and he'd think Felix would agree with him too and then show his surprise/anger when Felix isn't happy with the outcome.
There could be some mild jealousy that Felix has a family while he doesn't and attemps to put himself between Felix and his biological family. Felix and Claude were raised together which could make him view any biological sibling that Felix might have as a rival to Felix' love. Claude's negative attitude towards his own family could sour Felix' possible relationship with his brother or sister that he didn't grew up with since he spend his youth in the palace as Claude's companion. Claude would be like "blood brothers don't mean anything because they can betray you unlike sworn brothers who have chosen each other. Our bond transcends family I want you to choose always me just like I have chosen you." Felix seeing Claude's words confirmed when Anastacius tries to kill Claude despite them having once been close to each other would make him aware that getting along with your legitimate sibling means nothing once you have become threat to their position by simply being better or more likeable than them. This experience might cause him to be more mindful of his words and actions around his siblings and the duke which would kind of eliminate the possibility of a fully equal and honest relationship.
Basically I can only imagine Claude x Felix just like in the hypothetical Claude x Diana x Felix AU I've talked about once. It starts out sweet and innocent then turns disfunctionally functional and then when someone else enters the stage who could "steal" Felix away it turns into something grotesque and violating.
I also can't see Claude and Felix doing cliche couple activities like cuddling or going on picnic dates or boat trips. For Claude intimacy would be murdering their enemies/ pushing Felix' moral bounderies/ making him sacrifice things for him/ making him vow his eternal loyality to him/ showing each others worst side to the other and still being loved. It doesn't necessarily have to include sex, although I like to headcanon that they fucked after Felix committed the massacre that earned him the name Knight of Crimson Blood, and they totally had a few "in another lifetime" moments during the dynastic revolution. I hc that Claude sometimes misses the time when their mothers died and their codependency peaked. The time when they were fighting against Anastacius' troops and he didn't have to think, he could just kill people to heart's content and it was just him and Felix against the world. Back then Felix didn't pretend to be any better and tried to get him to stop.