<<. Do not want to reinstall the Mail app and lose my saved emails. >>
if your mail accounts are set up as IMAP, so that you can read emails on your iPhone or another device as well, the emails themselves are NOT stored on your Mac at all, except in "on My Mac" folders. the bodies of the emails are stored on the IMAP server(s) of your service prob=viders, and the subject's (only) are sent to you for display in a list. when you want to actually READ and email, the server downloads it to you at that moment.
This means that deleting an IMAP Account and re-adding it is intended to have no impact on your emails or anything else.
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if you are running MacOS 11 Big Sur or later, there is no longer any added value of just re-installing MacOS in place (which is intended to not touch YOUR files in any way.) MacOS does not modify itself. The system files are on a crypto-locked system volume that can not be modified by ordinary means, and if modified, MacOS can determine that very quickly.
Another classic debugging method that can be modestly useful to help isolate Hardware issues, is to make one or several backups, then ERASE the boot drive and re-install. Testing at that moment, when ONLY standard MacOS is present and no third-party add-ons have been installed, can help isolate Hardware issues, but yours is not Likely Hardware.
What MAY be helpful is an Etrecheck report, especially from then the problem is happening.
Consider downloading and running this little "discovery" utility, Etrecheck. It changes NOTHING. Etrecheck was developed by senior contributor here, and uses system calls to collect often-needed information.
it contains little tests for speeds of devices, CPU utilization, memory usage, energy usage and a digest of recent problems, in one easy to use package. it does not even need to be Installed. Because less can be learned when your Mac is running great, best time to run is when your problems are actually occurring, if possible.
if you follow the directions faithfully, its report (pre-laundered of all personally-identifiable information) can be "Shared" to the system ClipBoard, then Pasted into an ‘Additional Text’ window in a reply on the forums.
How to use Etrecheck pro for free
http://etrecheck.com

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