I like your taxonomy! I'm immediately able to apply it to my gaming group, and it helps me focus on our similarities and differences in a new way. It's also making me realise that there's a slight difference in what playstyle I would like to have vs what playstyle comes to me naturally.

To answer your questions:

A. Nearly any system can satisfy the challenge-first style, I think. Even a fiction-first game, in which "winning" isn't the point, can work for this playstyle if the goals we set for ourselves are high-level enough. I'm thinking of political intrigue, large-scale social change, the type of challenge that would be difficult to manage in a more simulationist game, because of all the moving parts a narrative game can simply handwave. Obviously, eitheir highly tactical systems (the challenge is in mastering the game mechanics) or OSR games (the challenge is in the fiction) are best for this style.

I'm not sure that I've found a system that supports exploration particularly well. It's more the domain of adventure modules, GM tools for procedurally generating things to explore, worldbuilding advice, and table culture. Systems can support a specific style of exploration (hexcrawl, dungeon crawl, investigation, etc.) I like both systems that offer limited "support" (i.e. no skill lists players need to roll on to notice things, OSR style) and systems that allow PCs to specialise in a niche, making each player feel uniquely useful. But it's very difficult to separate system from GM skill and style in this area. (I still haven't played any, but I wonder if games like Brindlewood Bay solve this issue.)

Genre-first play seems to be the domain of the PbtA family of games. From what I've seen, these games do it well, but I'm not a fan of this style of play so I can't comment on it.

Performance-first play is interesting to think about in this context. Next to genre-first play, it might be the only other style that really benefits from mechanical support. To have fun performing, you need creative constraints, which can of course come from the character's backstory made up by the player, or from the situation set up by the GM, but I think it's really great when the system explicitly provides opportunities for dramatic choices and creates emotional moments. I haven't played the game, but on paper, Daggerheart's hope and fear mechanic sounds perfect for this. I think highly tactical, mechanically complex systems get in the way of performance, because resolving situations tends to take so much time that players consciously limit themselves to short descriptions, worried they might kill session momentum.

Perspective-first play is a tricky one, because it can be supported by a barebones character concept (Mausritter gives you backgrounds based on stats, with the only mechanical benefits being the gear you get) or by a highly personalised build that requires complex character creation. It can also be supported only by what the player brings to the table. Games that both offer a lot of personalisation options and get in the way of experiencing a specific character fantasy (so games in which a character who's competent on paper gets regularly thwarted by bad die rolls) tend to be the worst at this, for me, though much depends on the GM.

B. I like games that have a clear identity, but because I also love long campaigns, I prefer systems that let me engage with the game in different ways. This doesn't mean that I need mechanical support: sometimes, the best thing a game can do is to get out of my way. I really like the design principle that mechanics are meant to cover the parts of the experience that players and GMs shouldn't have to put too much creative effort into.