Any clue as to why yet?

You have Mojave 10.14.3. The last version of Mojave is 10.14.6. You have the first version of FCP 10.4. If you updated to Mojave 10.14.6 you could update FCP to 10.4.10. Even if you can't you should be able to update FCP to at least 10.4.6. There are a lot of bug fixes since the first version of FCP 10.4, which was almost three years ago.

The OS is updated in the Software Update in System Preferences. If it shows you Catalina, there should be a link to More that will give you other options.

The application is updated in the App Store. You need to be signed in with the Apple ID used to buy the application.

Exact same issue as what?

What’s the computer exactly? What’s the OS, the FCP version? What are the project properties?

Trash the preferences whenever the application crashes.

Will the computer update further, to 10.14.6? Can you update the application any further?

Are you trashing your preferences after the application crashes?

Try making a new admin user and testing the application there.