The good news: I have gained control over LO via CafeTran Espresso :).
I took the plunge and deleted CafeTran.app and LO and installed them both again. My license is still active.
Now I have the CafeTran Espresso app on my macOS Big Sur the way you intended it to look.
I can exploit two scenarios to restore my settings:
I restored the settings manually!
BTW: Perhaps a check if a preview document already has been opened in LO would make sense?
And perhaps (perhaps!) a setting to close the LO preview when CafeTran Espresso quits? (Can add this myself via Keyboard Maestro.)