Remote access works for several minutes then goes offline and Plex Server crashes

So it continues with a clean install.

For reference, Plex has PMS Uninstall Instructions in their articles.
You would have to do all of them, and I made a script to automate it.

Script to Completely Uninstall PMS for Mac

#!/bin/bash

rm -rf /Applications/Plex\ Media\ Server.app && echo '[1/5] deleted the app'
rm -f ~/Library/Preferences/com.plexapp.plexmediaserver.plist && echo '[2/5] deleted the plist'
rm -rf ~/Library/Logs/Plex\ Media\ Server && echo '[3/5] deleted the logs'
rm -rf ~/Library/Caches/PlexMediaServer && echo '[4/5] deleted the caches'
rm -rf ~/Library/Application\ Support/Plex\ Media\ Server && echo '[5/5] deleted the application support'

echo 'Two manual steps are required to remove all traces of PMS on your Mac.'
echo '  * Use the link to remove the Mac from your Authorized Devices - Server.'
echo '  * Empty your Trash and restart the Mac.'
echo ' '
echo '          https://app.plex.tv/desktop#!/settings/devices/pms'
echo ' '

I wouldn’t reinstall MacOS just yet. I would ask Apple for help to identify the cause.
Tell them you have an app that used to work but becomes unresponsive every 30min.
Tell them you don’t remember changing anything.
Tell them you completely uninstalled it and reinstalled it with the same result.
Tell them the app is known to work on your Hardware and MacOS. I use it every day.
Tell them we need help finding any system message telling us what’s wrong.

We might get lucky.

If I decided to try a fresh install of MacOS, I would clone my Mac hard drive using SuperDuper, then I’d wipe it and reinstall MacOS and PMS to see if that fixed the issue. If not then restore the Clone. No reason to nuke your system.

Good luck!