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Question, does your monitor have a KVM? Cause I definitely notice this behavior, even on windows and os x with my monitor. I believe it was the same way on linux as well but it's been a minute since I used linux on my desktop
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This is actually a laptop with its builtin display.

Edit to add: I don't think it has too much to do with display latency.

It is some convolution of the desktop environment and display server deciding that keyboard input doesn't go to the focused window while it is in this nominal screen blank state. This Fedora 43 on a boring generic Thinkpad.

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