Users who want to read chat messages can either enter the room they were posted in or view its transcript. Only the former category show up in the room's sidebar. Is there any way we can see that people are reading a room's transcript, and/or add them to the sidebar?
No, we normal users (and I assume this goes for moderators as well) can't see who got served a page to their device. Only devs or sysops could know.
And I want to keep it that way. I use the feature to check on SPAM posts and I don't want to disturb the room by entering it.
You might have overlooked anonymous users. They can read the transscript as well, do you expect something to be shown in the sidebar as well for them?
Suppose we do know who is reading the transscript, for what purpose are you going to use that fact?