Hello,
I followed your raised question and here are some fixes for your Mac but first of all, I would have to tell you to not downgrade to Catalina because Catalina's support is ended and apple is fully concentrated on Mac Big Sur, to keep in touch with apple's movement and latest features, I highly suggest you stay with Mac Big Sur.
Here are some fixes that worked with my 2017 iMac which came with Mac Catalina when I first got it, now I have Big Sur and it's as smooth as butter.
Enable reduce motion through accessibility (This will help reduce or perhaps fully stop your map from lagging. If you still face slowing/lagging/glitching issues, you can also reduce transparency which will help for sure but won't look as good).
Make sure to get CleanMyMac and run all of its free programs (You can also get paid version if you want)
If you just recently updated to macOS Big Sur and you feel the Mac is slower than usual, the best course of action is to keep the Mac awake, plugged in (if it’s a laptop), and let it sit for a while (perhaps overnight or for a nights) – basically, hurry up and wait. I know that sounds like weird advice, but here’s the logic behind it: after a major macOS system software update, the Mac performs various maintenance routines behind the scenes, it reindexes the drive for Spotlight and Siri and apps like Photos may reindex too. So basically, let the Mac sit turned on overnight, perhaps for a few nights in a row, and allow those indexing and optimization processes to complete. When they’re finished, the performance of the Mac should be significantly better, if not entirely back to normal. This is often the number one reasons Mac users think a new operating system is slower than a prior version, so don’t disregard this simple advice!
You should also get firefox instead of using chrome (if you do) because chrome can slow your mac very much and plays key part, especially on Mac Big Sur. Firefox is one of the Top 3 browsers and it's very smooth.
Taking these steps has helped me significantly to reduce total lag and other slowing issues. In-fact, my iMac now runs better with Mac Big Sur compared to Catalina.