I've had a similar issue, things appear to randomly double click. Most strangely, right clicking sometimes appears to trigger a double left click (I think it might be a right click followed by a phantom left click).
Often Ctrl+V will paste more than once.
Sometimes keystrokes seem to be out of order (arrows and letters and pasting). There is nothing quite as mind bending as typing, pressing an arrow key and pasting and having your paste end up in the middle of what you typed.
I can't be sure exactly when it started, but for me it was around the release of windows 2004. My destination was updated to 2004 and the client was updated to 1909 at about the same time. Its persisted with the destination updated to 20H2 and I've tried updating my RDP client to 1.2.1755 but the issue persists.
I'm running it as a remote app, I tried various settings in the RDP file. I even disabled UDP thinking packets were getting reordered. Latency is typically around 30ms but I wonder if this issue is related to lag spikes / jitter or something.