When pressing cmd+tab when the Illustrator is an active app, it only changes the top default panel with the name of the app, but the Illustrator stays as an active window. When I click on any app icon on the dock panel it acts the same way. The only way to change the focus to the app I need after Illustrator is to click on the other app icon twice in the dock.
Adding my corroboration that this bug still persists months after this original post, and in a different configuration. I'm running macOS Catalina 10.15.7 on a 3.2 GHz Intel i7 2018 Mac Mini @ 64GB RAM (paired to an RX 580 eGPU).
It's so disruptive that I've had to downgrade from Illustrator v.26.2.1 to v.25.4.1 just to get any work done.
For anyone trying to test/reproduce this, make sure you have Illustrator in Full-Screen Mode.