FCPx crashes when exporting from external drive only

Is Prey running all the time? Reboot without reopening applications. Open only FCP and try the export. You might also try testing a new admin user. You have a lot of plugins. Are they from FxFactory or other vendors? Plugins often run into problems with OS updates. The kernel panics are a serious cause for concern as everything on the computer should be sandboxed from the system, especially in Catalina.

How’s the GDrive formatted?

You should generate an EtreCheck report using full drive access from the application preferences. Copy the report and paste it using the Additional Text button.  The application is a free download from the App Store. 

When you export from the GDrive is the export going to the GDrive? If so, what happens if you export from the GDrive to the internal drive?

Configuration Profiles:

This computer has configuration profiles installed.

This is unusual. Configuration profiles are typically only used in machines that are managed as part of an installation - like a school lab, for instance. Other than that, they may indicate the presence of adware.

Do you know what these profiles are?

If you go to System Preferences, is there a Profiles pane? In a "normal" Mac, there isn't one...

I agree with Luis about Tom. I think it's worth a try to uninstall Prey and 3rd party plugins to see if there isn't some incompatibility with Catalina. You might also try the Catalina Combo Updater to repair/reinstall any files that Prey may have modified. https://support.apple.com/kb/DL2040?locale=en_US Good luck and keep us posted on your progress.

Two thoughts:

1) Make sure that FCP has "Full Disk Access" in System Preferences->Security & Privacy->Privacy

(it probably already does, but it's worth confirming)

2) I'd try uninstalling Prey and see if it makes a difference. "Security" applications often seem to conflict with professional applications. If it proves not to make a difference, you can always reinstall it.

Note: I am not familiar with this application, and it may be quite proper and fine, but it seems like the most obvious suspect.

From everything you’ve said I’m not sure you can point to a single cause in every instance. The kernel panic usually points to a hardware malfunction which is why I recommended reducing your system functions to a minimum during the process.

How much free space left on the external drive?

I’d be surprised if the GDrive is failing. There are quite a few other plugins that I don’t know.

Don’t know what Prey does or what startup items you have, but anything that’s reading files and checking them while files are being written should be suspect. Anything that’s reading partially written files and making system calls OS problem.

New computer is a difficult question. Now might not be a bad time. It looks unlikely that there’ll be pro model updates until next year and then likely first generation Apple Silicon systems, which is a bit of a gamble.