I have the same issue. Once I put apps into split view, the iPad no longer detects keystrokes from my smart keyboard, even if I’ve touched the screen to select the app and have an active cursor input box selected. I have to turn off the iPad screen and then turn it back on and it will start registering keystrokes again.
the trackpad continues to operate without issue. It’s almost as if the iPad can’t determine which app has been selected and requires a screen power cycle to reset.
I’ve tried Apple’s magic keyboard and Logitech’s Combo Touch and both experience the same issue. This isn’t something I only experienced with the new iPad OS 15. this has been an issue with OS 14 too.