I don’t know if this is a bug or not, but when I have two projects open, Dorico behaves if I have clicked and held the main button down in the background window. Pressing escape doesn’t release it, it only releases when I click the window, click again and selects something and press escape.
I have exactly the same issue
Because Dorico has to unload and reload the VST instruments in each project when you switch between them, sometimes the mouse-up of the click that activates the window can get swallowed as the interface is momentarily blocked while the loading starts. You should find that clicking again is sufficient to put things right, i.e. another mouse-down and mouse-up should be sufficient to clear things. It doesn’t happen often for me on my Mac, but it’s a bit newer and possibly faster than yours (mine is a 2018 MacBook Pro).
Same issue; becomes often: MacBook Air 2013.