Screen Sharing overlay causes freezing of System Controlling

Hello. When I try to share my screen with different applications (Discord, Google Chrome/Firefox, Safari, Telegram, etc), it causes a total freeze of Selecting Window overlay. I can't even click on any button on this overlay, I can't type anything in applications, some windows are blinking. The only thing working - touchpad gestures and maybe opening application by clicking on it in Dock, but I can't even click any element inside this application. I haven't found exactly the same problem online, but similar topics share solutions like `Disable Remote Management` doesn't solve the problem, because Remote Management is disabled in my system. Sometimes Screen Sharing works, but only if I do hard-reboot on this freeze. Also it may unfreeze in 1-10 minutes (can't detect how much long I need to wait until it unfreezes), and then it may have 2 ways - it may share screen after some time, or it may crash screen-sharing options. I have recorded one of these sharing problems, and during this screencast I can't stop the recording. I don't know what is the reason why it happening, but it starts to happen after I updated to Sequoia, where this overlay for screensharing appeared.

MacBook Air 13" 2020 16/256, macOS 15.1.1

https://www.youtube.com/watch?v=m6mZCo80Dfc