I've tried to use an Android device as a desktop replacement before, but the input lag is always there and it's really annoying, even when using a wired USB keyboard. It seems that input lag is an intrinsic characteristic of an Android device.
How long would you say this input lag was? Like how many milliseconds? Some people, especially non-gamers, just "don't see" lag unless it's significant. So you could be right that there is lag even if others don't see.
I'm using a physical keyboard on the nothing phone and I don't have any input lag problem. I am using it mainly for termux admittedly but I haven't perceived any in other apps.
I just tested it out and it didn't work well for me. It reliably started either on the current app or on the latest app when on the home screen but I haven't managed to change windows at all. That could be due to my weird keyboard though. It only has 34 keys and has a weird way to reach the alt key which might be messing with everything.
I'll see if I can try with a standard keyboard later.