apple air with logitech keyboad case

I recently purchased an apple ipad air(M2,2024) along with a logictech Combo touch keyboard case.

The keyboard space bar and arrow keys Do Not Work with the ipad air. I have rebooted several times but the problem does not stop. The so Called 'genus' at apple said there is no problem and told me to purchase a more expensive case. Don't purchase these products from an apple store as they don't guarantee their products.