When navigating through the forum, when I go to some topic, the first thing playroom reports is that by pressing CTRL+R I can reply to it, CTRL+N starts a new discussion and CTRL+T shows a list of participants. All shortcuts work except CTRL+T. Pressing it doesn't make any action. However, when I open just a category, CTRL+T informs about the last time a new answer was published.

Hello,
this shortcut is valid only for your inbox/your permanent messages.

If you use it there, it will announce everybody participating in the current private discussion you have opened.
On the forum, it has no function since there is no concept of participants, anybody can reply to any topic.

CTRL+T in any forum doesn't actually do anything, on my side it just does whatever CTRL+T should do in the current context, such as announce the duration of the current game or the server uptime if I am in the main room, so I am not sure which time you are hearing, but it's probably not the time of the latest reply.