Very annoying the drive client does this. I have this same issue everytime I (manually) renew my cert. The problem goes away when pausing and resuming the sync.
The next time my cert expires I'm going to try and stop the Drive package on my NAS, replace the cert with the new one then start the Drive package again. Then see if the clients then accept the new cert after establishing a new connection without a stupid warning where I'm like:
If you’re computer stays on the local lan is ok to continue to use the local ip. You’ll get a certificate pop up, just choose no. I have 2 desktop computers using the local ip and it has been flawless for months; same goes for the active backup app.