So I have actually experienced this bug many times in the past years, though it felt really random / rare when it happened, so much that sometimes I would think it was fixed until it happened again.

However I just found out what causes this issue, this is easily re-produceable on the latest iOS steam link version, windows 11, and latest steam client version. If you have the keyboard settings on iOS that changes 3 periods into a single character of 3 periods (smart punctuation, on by default), it causes this bug to happen every time. Basically simply typing “...”-> which turns it into a single character “…” anywhere on the pc at any point seems to cause this bug to happen. All applications except for the one you are currently tabbed into become un-interactive. You cannot click into, type into, or alt tab into them even when you end the remote connection and you use the physical mouse and keyboard. It also happens if you double tap space bar on the iOS keyboard after any word, with the setting where it automatically adds a period to the word. Most of these settings are on by default for iOS users.

Afaik the only way I can get windows to completely recover from this state is by resetting the PC. You can sometimes get other applications to be interactive but seemingly only after you close the one application you were able to interact with, then it moves to another app, but all other apps even the desktop are still un-interactive.