Hi,
Frustrating situation indeed. I have seen lots of issues with the move to Catalina and updates to Logic that are related to legacy/unsupported drivers and plugins causing issues in the pure 64 bit environment.. Our computers tend to collect all sorts of interfacing code with every device that is plugged in over the years. Lets face it we tend to be packrats with plugins and other kit!
I would suggest the following to try and help you to isolate the issue and resolve:
1) Update Logic, current version is 10.6.3 and and the update could help clean up and refresh various files related to Logic.
2) Make sure that ANY MIDI and Device drivers are up to date and SUPPORT Catalina. This is REALLY important since many legacy drivers have issues with Catalina.
3) Review ( using Plugin Manager ) all your plugins and remove any that have failed validation. Note any you remove and scrub the drive for any related files.
4) Make sure any third party plugins are up to date and support Catalina and latest Logic
5) Run Disk First Aid to make sure there are no drive or permission issues
6) Run a memory test to make sure there are no issues with the RAM
7) Check in Control surfaces and delete any old/unused "control surfaces" that have been added over the years. Note any you remove and scrub the drive for any related files.
7) In the Apple Audio Midi Setup delete any unused Audio or MIDI interfaces. Note any you delete and scrub the drive for any related files.
8) If using an external drive test with the project on the Internal drive. This could identify drive pr hub issues.
9) Disconnect any external kit that is not needed when working on your session. Only add as needed and watch for a pattern related to the issue.
Many crash issue are related to third party software and a good cleaning can usually resolve issues.
Hope this helps.
( If this was helpful please mark as such or mark as solved if that is the case )