Reporting
Sometimes stuff in meeting rooms break. This needs to be easy for people to report, like "the projector is not working", "speaker phone not working", "room very dirty" or whatever we can think of.
This information needs to be stored somewhere, in a database or something, so it can be cleared once it is fixed - and somebody should be notified about it (facility management DL, email or whatever).
Notification for other bookers
If I have booked a meeting room, that is now marked with an issue, I should get a notification. Preferably while booking, it would be visible in the interface, but if not, then maybe I would get an email stating the issue, so I can consider rebooking.
The question
Does software like this exist, maybe even some functionality in Exchange/Outlook, that I am not aware of? Third-party?
This is likely to be closed as it is more of a "software recommendation" question as it is currently written. You may be able to wordsmith your question better to avoid that, not sure.
That said, there is no built in functionality within Exchange to do this, but you could look at programmatically doing what you want.
A possible solution (logically) would look like this:
These types of things can be accomplished but it would require Exchange scripting that is beyond the scope of a quick answer here...
I'm not aware of any. You could probably get something together if you bring in Microsoft Flow or PowerApp. You could create a SharePoint list for tracking submissions, and wire up flow to take action when new items are added to the calendar, that checks against that SP list.
Flow is still evolving, and I know it has a check for new items being added to a calendar, but have not dug in deep enough to provide a more detailed solution.
Outside of that, you may have to custom code or script something that handles the interaction.