When Refresh was originally released, it was only available in the "default" profile. Over the years, profiling has evolved, so I'm not sure whether that is still the case, but please check here:

Inside Firefox, type or paste about:profiles in the address bar and press Enter/Return to load it.

Take a quick glance at the page and find the Profile has this notation: This is the profile in use and it cannot be deleted. That is your currently running profile.

If that profile has a Set as Default Profile button, go ahead and click that. If it doesn't, then your currently running profile is already your default profile.

I'm not sure you'll see any change to the Troubleshooting Information page immediately, but hopefully after your next regular Exit/Restart it will appear.

Firefox Sync will transfer your bookmarks to a new computer only if they were successfully synced beforehand, but the error you’re seeing means your new profile’s bookmarks database is corrupted or locked. To fix it, close Firefox and rename the `places.sqlite` files in your profile so Firefox can create clean ones on the next launch; once the database loads normally, Sync should restore your bookmarks if they were backed up to your account. If they weren’t synced, you’ll need to recover them from your old Windows 10 Firefox profile or a saved backup.