Final Cut Pro X - Not Enough Disk Space Available to Process Clips

Does FCP have Full Disk Access enabled in System Preferences?

Did you try resetting FCP Prefs? Hold option and command while launching FCP and choose Delete Preferences. It will open the default Untitled library. Re-open the library you were working on, set the preferences back to the way you like them (disable background rendering, reset Import to Leave Files in Place, etc.) and see if the issue has been resolved.

Did you dismount and disconnect the ExFAT drive?

If you still have issues, post an https://etrecheck.com report after giving it Full Disk Access. Use the "Additional text" button below in your reply to paste the report.

Chrome and its keystone daemons are installed. Chrome breaks the video toolbox and the daemons are known causes of ProApps problems. To completely remove, follow the instructions at https://chromeisbad.com and then you'll need to reinstall FCP.

Do you have 3rd party plugins and are they up-to-date? There are some popular ones that are not yet compatible with M1.

Full Disk Access in System Preferences->Security & Privacy->Privacy

Full Disk Access needs to be set for FCP and other applications that access the system. This is in Privacy System Preferences. If the applications aren't there, click the + button to add them.

If there are no problems with fresh library, then I'd look at some sort of corruption in the problem library or project. You can open the problem project's timeline, select all, copy, then paste it into a new, blank project in the freshly created library. This sometimes clears odd corruption issues. It's also possible some media has become corrupt.

Did you try copying the bad project contents into a new project?

I don't know what your timeline looks like but if it's primarily the multicam, I think you could copy the edited bad multicam and paste into your new timeline lined up above the good multicam. Disable the bad multicam and just advance to each edit in the bad multicam and make an edit to match in the good multicam. Basically the bad multicam is just acting as a guide.

If that doesn't work, there might be a geeky way to recover your multicam cuts by editing an exported XML. I haven't tried it so this is conjecture, but I think you'd export an XML of the bad project and an XML of a simple project containing only the good multicam. The open both XMLs in a text editor and note the reference to the good mulitcam. In the bad project XML, change the bad multicam references to the good multicam. Then import the edited XML.

FCP can't work with ExFAT. Remove that drive and see if things improve.

Your system drive is basically full. It needs a minimum of 10% free, preferably 15%.

Please post an Etrecheck report from https://etrecheck.com, which will provide information about what might be going on. Give the application Full Disk Access in Privacy System Preferences, and use the "Additional text" button at the bottom of the reply box to paste the copied report. 

Please post how large each of your drives are, how they are formatted, how they are connected and how much free space is available on each. Don't forget to include the system drive.

How are they formatted? (APFS? HFS+? ExFAT? NTFS?)

Give EtreCheck Full Disk Access and post another report.