Since I posted this thread I did some digging on my own.
I’d had trouble with NoMachine previously, as described in this thread: https://forum.nomachine.com/topic/mint21-no-mouse-wheel-scroll-in-some-applications.
It’s the same machine. The setting suggested in that thread now causes my new issue. Removing this setting fixes server not registering input; however, it restores the original problem of the linked thread.
Technically, the original problem is much lower in severity than not receiving any inputs, however ideally I would like to solve both.