I've been seeing this same issue for the past few weeks. I'm using Mac OS 12.7 and RDC 10.9.3. It started when I updated RDC a few weeks ago and hoped that one of the bug fixes since then would have fixed it but the problem is continuing to happen. I get a beach ball when copying from a Windows environment and pasting the content into various Mac apps including Text Edit, Slack and Chrome. It happens at least once per day. It could work five times in a row normally and then suddenly, I get a beach ball and the app I'm trying to paste into becomes non-responsive for about 30-60 seconds. It will typically clear and then start working again for me.
I've also noticed some trouble copying from the Mac and into the Windows login prompt as well recently but I'm not sure if that's related or not.