The breakout doesn't function in full screen mode on Windows 10. There is a white screen with music playing. Alt-tab out and back and the title screen appears but the mouse cursor doesn't move.

Gog (Galaxy) installation installs Java 7 Update 40 (64-bit). I tried more recent versions of Java 7 and Java 8 based on other forum posts on Gog/Steam to no avail.

It seems the only solutions are to run windowed (too small for me) or set the desktop resolution to 800x600, after which full screen works correctly.

I previously played through Harvey's New Eyes without issue (though on my Mac). Hoping The Breakout gets patched.

I sent a message to Daedalic support about this issue, and suggest you do the same.

Idem for me. I wanted to keep my Java 8 version, and I got a white screen on start, in fullscreen mode.

Yes, the same happens to me. I just installed it recently.
I've tried 800x600 but it did not work for me. Also tried multiple compatibility modes but none of those work either.