For others wo come across this:
During the update, the old version of YouniqMail didn't shut down cleanly. It's still holding the database locked while the new version tries to start in parallel. That's why the startup hangs without ever showing a window, leaving you no option but Force Quit.
How to get the app running again (on MacOS):
Quit all YouniqMail processes: Open Activity Monitor (Cmd+Space → "Activity Monitor"), search for "YouniqMail" and quit all entries (including any "Helper" processes).
Maybe just to be safe, restart your Mac/Computer that guarantees no leftover from the old version is still holding the database lock.
Start YouniqMail as usual.
After that everything should work again, and no data will be lost.
A fix is already ready and will be in the next version included.