Target display mode not working

Hi,

I have a iMac 21.5 late 2012 on macOS Catalina 10.15.7

and a MacBook Air M1 on Ventura 13.5.2

And I try to use my iMac as an external monitor by target display mode.

I've connected them via thunderbolt: iMac - thunderbolt 2 cable - thunderbolt 3 to 2 adapter - MacBook

I press command+F2 on iMac and nothing happens. I press Fn+command+F2 on iMacand nothing happens.

Or rather my iMac makes a beep. I had check success connection in system information.app. Each Mac see the other Mac in the Thunderbolt tab of System Information.app. I have press command+F2 and Fn+command+F2 but nothing still works.

Thanks.