I very much do agree that Sheila and Fugo banter/argue quite a bit as enrichment, but I don't believe it's because either of them is argumentative by nature.
In Sheila's case, I think she sometimes pushes buttons to test boundaries and as a way to reassess if the trust she bears for the person is deserved AKA if they don't go off on her, belittle her, respect when she distances herself and walks away etc. She's also equally stubborn about the things she's right about and about the things she's wrong about, and unless it's a matter that strikes a personal note, she never cares either way, it's not a competition to her. If she's right, then she was always right, if she's wrong, she will literally just walk away and move on with her life, much to the fury of whoever she's been unintentionally ragebaiting for the past 10 minutes. I wouldn't necessarily call her contrarian for the sake of it, but her general strategy for petty arguments is to be purely reactionary and disagreeing with what the other person says and then standing her ground no matter what, with virtually no stakes in the game. Ultimately, for her it's a means of enrichment and Quality Time together, unbeknownst to whoever decides to engage with her with the intent of proving her wrong or changing her mind.
As for Fugo, I don't think he ever really starts playful arguments and his attempts at banter are subpar. He engages with everything genuinely (unless he has an exceptionally playful day and shamelessly shoots those subpar attempts at banter), which means he's, at the core, just trying to help and/or get the record straight rather than come out on top. He's quite ragebaitable, however, except he's got the spine of an invertebrate and will drop the issue if the other party walks off (figuratively or literally) or if they disapprovingly comment on him taking it too seriously, then he gets embarrassed and walks off himself. The way he finds himself in spats is that he either says something factually incorrect (more often than he's given credit for) or when he wants to politely inform that he doesn't think what someone else has said is the case. Either way, he's losing against Sheila.
All this to say, I think their banter stands on Sheila enjoying having someone who's willing to engage her as she wishes but will fold the moment she's bored or wants to move on to something else, and Fugo I think enjoys the fact Sheila's not afraid to poke fun at him or challenge him on stuff because it makes him feel normal and secure in being allowed to be wrong and petty and annoyed and preening from pride in the one in a million instance where he's right and she lets him have it.
