Well, if neither 4K or high frequency is actually a requirement, then https://jetkvm.com/blog/introducing-jetkvm-mini would maybe fit.

It is 4K, just not the 120Hz or higher gaming grade the parent was asking for, and better than the 1080p of the JetKVM Mini. The JetKVM Mini does offer Ethernet, however (not sure if it can be powered by PoE, however, which would be a huge plus).