[2022] Whenever a new champion comes out, I have absolutely no desire to play them but I often despise playing against them. Is the game just not for me anymore?

I see folks also use the wiki as their source of info for learning what a new champ does from scratch, which it's not the best at since it has way more detail than is really needed to get going. The client is a better resource for this since that's what we write those short descriptions and include videos for. Once you have the basic grasp of what a character does, the wiki is great for hunting down the details if you want to get into optimizing playing as and against. For all that Bel'Veth passive text, the client description is

Bel'veth gains permanent attack speed stacks after taking down large minions and monsters and champions. She also gains temporary bonus attack speed after using an ability.

and that's enough detail to grasp it. If you're now interested in "how do I optimally cycle my abilities to keep passive uptime", or "how does Riot numerically tune infinitely scaling attack speed" you can read the wiki version.