Get a shell on Exchange Online by following Microsoft's guide.
Publish the calendar for the room:
Set-MailboxCalendarFolder RoomNameHere:\Calendar -DetailLevel fulldetails -PublishEnabled $true -reseturl
Show the .html link, as well as the .ics link:
Get-MailboxCalendarFolder -Identity RoomNameHere:\calendar
This also works for sharing user's calendars. The key to seeing all of the details instead of just "Busy" is the aptly named -DetailLevel fulldetails
.
I was helped by Miles Hayler's answer on superuser.