Texting is very sluggish on 2020 iMac running Big Sur
If it's just in Messages.app, I would check two things:

network traffic to/from the app,
try doing an 'inspect' of the process while it is exhibiting the behavior (in Activity Monitor). Do one before it has the problem, so that you have a baseline.
your keyboard connection (bluetooth or USB) and see if something else is interfering with it.

Since it's new, you should also definitely contact Apple, in case there's a hardware issue, which would be a warranty-covered problem. Also, their support specialists are quite good on the phone, in my experience; I've been happy to refer clients there and have not been embarrassed by the support they get. You are entitled to the support, you paid for it, enjoy it.