This is embarrassing but I now think Big Sur wasn't responsible for the choppiness on my machine at all. I had installed Adobe Creative Cloud shortly after updating to Big Sur. When I uninstalled Adobe Creative Cloud 7 days ago the choppiness completely vanished.
This is not an answer, but may help someone else. For about 3-4 days after updating to Big Sur, the cursor lurched across the screen, keyboard inputs took hundreds of milliseconds to appear on the screen (meaning I'd sometimes hit the key twice because I thought the first didn't register).
Approximately 4-7 days after the update, the behaviour disappeared entirely. I have not been able to explain why it happened (it never happened in Catalina, and it started immediately after updating to Big Sur, so I presume the update had something to do with it). And I also cannot explain why it stopped, except that it ceased 4-7 days after the update to Big Sur, without me doing anything.