While I had never problems using Crossover Office on Debian, a fresh install on a fresh Debian 12 Bookworm revealed that 32 bit dynamic libraries were missing -- I got message like:

Can't exec "bin/wineloader": No such file or directory at cxoffice/bin/wine line 1310.
wine:error: unable to start 'cxoffice/bin/wineloader': No such file or directory

To fix that, run:

cxoffice/bin/cxfix --auto

That should add the missing 32 bit libraries.

To check in addition for any other missing libraries: In the running crossover GUI:
Help -> System Information
to see if you are still missing any library. And indeed, still I needed to install apt install libcapi20-3 libosmesa6.

See also https://www.codeweavers.com/support/forums/general?t=26;msg=215738