When using my iPad Pro 12.9 to remote into my Macbook using my bluetooth Logitech K380 keyboard and Magic Trackpad 2, I can view and interact with the session as expected. However any time I try to use my external keyboard to enter text and hit the spacebar, the right control pane is activated and the space is ignored. Repeatedly hitting the spacebar closes running applications, it never actually enters a space in the selected application. This makes using Parallels Access basically useless if I can't actually type a space into anything. I've turned off the "Show Keyboard Automatically" option in settings, but can find no other options that might have a bearing on this behavior. I installed Parallels Access from the App Store last night, so I'm assuming it's the latest version. I also installed the Mac client this morning from Parallels directly, so it's the latest as well. Thanks for your help.
I'm seeing the same problem on 11" (3rd gen) iPad Pro running iPadOS 15.3 and using Apple's Magic Keyboard, and I think I've seen it on the larger iPad Pro of an earlier generation using its version of Apple's folio keyboard. A workaround I noticed: <shift> <space> instead of space. Not fun, but better than nothing.