I've found a way to do the puzzles in the study section after a fashion.
You can make the first move o.k and the reply is automatic.
To make a second move and every move after, you have to press the "hint" button.
It then highlights the piece you need to move and you can move.
It doesn't log errors or hints but at least it works that way.
I don't now think it's a chromebook issue now,cos I tried on the windows 11 PC and got the same result