Tough question regarding using MacOS from an External Drive.

I did this with a 2017 iMac to speed up everything with an external SSD connected via USB C

I formatted an external drive, then set the boot up drive to be the external drive . When I rebooted, I restored the OS to the default, then upgraded and got most of what I needed to restore my setup from iCloud backups. I could see the internal drive as available while running the OS from the external drive.

After running this way for several months, I eventually went back to the internal drive as the boot drive. I did this because the external drive occasionally hung up during boot up. I always wondered if USB C was the best way to connect. Some things I did on the external - like upgrading the OS - forced the internal drive to be the boot drive after rebooting. I found that my original internal drive ran much better after reformatting and reloading the OS. Fortunately, I have an M1 laptop and didn't depend on the iMac as a primary computer.

I didn't provide step-by-step instructions because I went back to the original setup and wanted to give you an overview.

About fans and fan noise in your Apple product - Apple Support

I'm betting that you already done these suggestions. I've found that over a long time and with a lot of changes, computers sometimes benefit from being wiped clean. Enough said by me. Good luck.

If you have the time and the option to experiment, you might want to consider reformatting the internal drive and starting from scratch. I know this sounds like a lot of work but I actually enjoyed the process. Maybe reformatting would solve the internal drive issues.

Look at the refurbished iMacs on the Apple site to get a like-new computer and save money. I've done it a few times.

You can't boot two OS versions simultaneously. It's strictly one or the other.

Use an external SSD as your startup disk … - Apple Community

You can see the internal drive but I wasn't able to copy and paste between them.

Will the internal drive pass a First Aid test?