WELL I'M GLAD YOU ASKED!!!! (pulls out book as thick as the english dictionary and the bible combined)
I'll start with Murat, then Bessi, then get to them together I guess
I feel like this first part isn't even a headcanon: Murat is hypersexual :sob:, I feel like he is the one typically "initiating" and it is easier for him to wear out Bessieres than it would be for Bessieres to wear him out. I feel like Murat would also be the one to introduce/suggest kinks. Also, imo Murat is the top, I know some people view Bessi as the top which is also a great view of it imo (there is no such thing as a bad view of bessimu). That being said tbh I'm not 100% sure what kind of top Murat would be, I'm not sure if he would be 100% dom I can see him giving Bessieres a more equal ground while still topping. I think Murat also gets very clumsy during foreplay w Bessieres because he's just happy to be with him.
For Bessieres I guess I don't have many headcanons, I feel like he bottoms but I can see them switching. I can see him being into like exhaustion/mindbreak to some extent :sob: maybe feeding into Murat's hypersexuality. I feel like even when bottoming he would still have a lot of control and influence over Murat, kinda seductress vibes. I also feel like Bessieres would be more prone to biting/scratching/leaving marks than Murat, although I do think Murat would leave some himself.
For headcanons for both of them, first of all, A LOT OF AFTERCARE!!!! VERY CARING VERY LOVING VERY CUTE VERY ADORABLE AFTERCARE!!!! Esp coming from Murat towards Bessieres, he just covers him in kisses and blabbers on and on about how much he loves him. Bessieres genuinely makes Murat happy and Murat wants to make sure he knows it (in more ways than one lolololol). I do feel like Murat would also try to cover Bessieres in kisses during the act as well, he is just very physically affectionate. I feel like Murat would be more vocal in bed but he would go out of his way to try to make Bessieres more vocal than him. I feel like they'd be open to trying out some kinks but def not hardcore/weird/unhygienic ones. I also think they'd both be very open to bondage tbh maybe has to do with the horse harnesses lmao.
Anyways that was 3 paragraphs about some of my deepest darkest thoughts about my OTP, enjoy, do with this information what you will I guess.