Mouse/Keyboard input mode: activate by moving cursor to screen corner and hide scrcpy window

- [x] I have checked that a similar [feature request](https://github.com/Genymobile/scrcpy/issues?q=is%3Aopen+is%3Aissue+label%3A%22feature+request%22) does not already exist.
Hey,

I was looking for an app to let me use my mouse and keyboard on my phone so fast and a bit like 'second display' apps.

I wondered whether I could use scrcpy for this purpose (I tried other third‑party apps and they didn't work well). I discovered I can do this with:
``` scrcpy --no-video --no-audio --mouse=uhid --keyboard=uhid ```
but it's not easy for me to use. Could you add a feature that lets me move the mouse to a screen corner to activate phone input, hides the small window that opens after running the command, and sends the app to the background? That way I wouldn't need to switch the active desktop tab to use the mouse and keyboard on the phone.

Start by reproducing the workflow with --no-video --no-audio --mouse=uhid --keyboard=uhid and observe the small window and focus behavior. Define done as activating phone input when the cursor reaches a screen corner, hiding the scrcpy window, and sending the app to the background without switching desktop tabs.

Written by the indexing model from the issue text.