Projects not exporting

In addition to this being the longest Etrecheck report I've ever seen, you've got some very old software installed -- Flip4Mac, Silverlight, Perian, etc. This typically means that you've been upgrading in-place for many, many years, and then migrated that old software to your new M1 MBP. Although it can take time, the way to reduce system problems and get the best performance is to do a clean install of macOS. First do a couple full backups, then wipe your MBP drive and do a clean install of macOS. Then migrate *only* the User data from the backup. Do not migrate Applications, Settings or anything else. Download fresh copies of the software you use from the App Store or 3rd parties.

You have multiple antivirus software installed. These can run constantly in the background and steal performance on production machines. The recommendation here is to run the built-in Apple software (which you are) and the MalwareBytes set to run manually or periodically, not constantly.

You also have the dreaded keystone software installed by Google. This is know to break the Video Toolbox and damages FCP. Completely uninstall Chrome and the keystone software that is scattered across your drive by following the instructions at https://chromeisbad.com Simply trashing Chrome.app is not enough. Once that's done, reinstall a fresh copy of FCP from the App Store.

Others may find more.

What are the project properties? What are the export settings you're using?

Please post an EtreCheck report https://etrecheck.com giving the application Full Disk Access in Privacy & Security System Settings. Copy the report and use the Add Text button to paste the result into reply box. 

Strongly agree with everything terryb said- and I have some good news for you.

In recent macs such as yours, you don’t need to completely erase your drive, because the OS is in a separate read-only volume. Hence the clean install is much simpler and quicker.

Make sure to have a current Time Machine backup.

System Settings->General->Transfer & Reset

choose Erase All Contents and Settings

When your mac restarts like for the first time, choose to import from another mac, drive or Time Machine backup; select your backup and CRUCIALLY check ONLY the user accounts.

Try Brave or Edge or Firefox. Never Chrome.

I don’t see why. Chrome is just a browser. Other browsers can access Google pages and online apps.