Maybe ignorance is bliss, since I came from a consumer router setup, but is it normal to have 200-900 active connections on a network of only 20 or so devices?
It depends on applications, for example if you run torrents there could be hundreds of connections just for a single client. Nowadays even for web browsing to perform better loading there could be many background connections to pre-fetch the contents.
No torrents on this end, but general browsing for sure. IPTVs, web browsers, Windows, etc.
Sounds like everything is as it should be.
As mentioned before, now many applications are not just running based on single connection (internet is fast now, we can afford multiple connections at the same time to serve better user experience)
For example, now I am at home, only 2 people, including laptop/phones only 14 devices and most are idling, I was just participated a video conference and OpenWrt is showing > 1000 connections during my meeting, it drops back to 100-200 when my call ends. From end user perspective you might think only 1 application in use however at background the video conference program is creating a lot more connections to do the job.
So when you say 20 devices with < 1K connections I think your network connectivity is kind of low already.