Magic Mouse and Magic Keyboard stops working in clamshell mode

I have a 16 inch M1 MacBook Pro and M2 MacBook Air. I use them both in clamshell mode with Magic Keyboard with Touch ID and Magic Mouse. Laptops are connected to Studio Display.

Usually on weekday mornings I pair mouse and keyboard with clients MacBook Pro, connect it to Studio Display, close the lid in MacBook, and start working. After I have stopped working, I turn off the bluetooth and disconnect Studio Displays cable. Then I pair keyboard and mouse with my personal MacBook Air and connect it to Studio Display.

Problem started first in MacBook Pro. When mouse and keyboard are paired, display cable connected and I close the lid, mouse cursor in Studio Display disappears and keyboard is not working. Sometimes cursor is visible and moves, but I can’t click anything. Couple of times there have been two cursor visible, and one moving. When I open the lid, cursor is visible again. Also if I have typed something with the keyboard, it appears.

Problem started with MacBook Pro in December. And now the same problem is also happening in my MacBook Air.

Only thing that fixes this, is a restart. But next time I wake them from sleep, and try to connect, problem appears again. So I have to restart both laptops once a day for them to work properly.

I have tried shutting them down completely. I have also disconected Studio Displays electric cable to reset it.

Both MacBooks have latest macOS Sonoma 14.2.1.

Does anyone have same problem? And does anyone know how to fix this?