I'm also having lag problems all of a sudden. I play The Sims 4, and prior to this, it has run beautifully. I've been able to switch between apps, run multiple things at a time, use Apple Music, use Safari, chat on iMessage, whatever. Suddenly, if I'm on the game, I can't so much as type a word without a multiple-second lag. All the fluidity between programs that I loved so much is flat-out gone.
Furthermore, even when that game is closed, my computer just doesn't run as well. It runs hot, and can't multitask like it used to be able to. The activity monitor says that, at worst, I'm using approximately 54% of my system at a given time. This wasn't an issue until Big Sur was downloaded onto my computer. I'm seriously considering going back to Catalina until it gets resolved. Why do we need a new OS every year, anyway?