When you're running lots of stuff behind a proxy, and you're older (like me), you can easily forget that not everything runs vanilla http(s) any more, that some things run via websockets. When you're running Home-Assistant and Node-Red to control your house, this is going to be a Big Deal :)
Today I learned that services running websockets need proxy version 1.1, not the default 1.0. That neither of these services like aggressive caching in front of them, and that there are some headers you pretty much must set to make them work effectively. Here are the links I followed for Home Assistant and for Node-Red, for those lost among you who stumble here.