So what is it for? If it's another inbox to check that's a bit of a productivity drain.
I could understand if it was explicitly designed to compete with other chat platforms. This would seem to fit with Fossil's mission well.
Then the core members don't need to have a dedicated channel somewhere else. If they did, then that would be another inbox to check; instead they can check the fossil chat when they are on the project site looking over commits or documentation.
So it is just another source of information on the main "fossil channel" instead of another channel to check. Viewing it in that way, it is reducing the number of channels by simply inlining it.
But isn't that "a replacement"?
I could see this as a useful feature when you need to chat with contributors once in a while in a less-formal way than issue comments.
It's not an instant messenger, more like a mail box or a bulletin board. Which works when network is down.
Fossil works offline! But leaving a local server up is pretty normal, and that way you get new stuff just as soon as other servers publish it.
Also, and unique to fossil, the server is just... fossil, same fossil that runs locally. No Gogs, no Gitlab, just your fossil, their fossil, and fossil on the server, maybe with a "real" webserver in front of it, maybe not.
The chat room is clearly intended to be run on an always-on server instance, but there's nothing stopping you from setting it up locally and inviting people to jump on your IP. Well, NAT might well be stopping you... but in principle!