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My understanding is that you want to book a recurring meeting for a month.Please point out any misunderstandings
When you are booking a recurring meeting , It will show the number of days available out of the total number of days booked:
If the room is not available at one day ,and there is a new request booking the room, a warning will appear like this:
When you are booking a meeting ,you can use Scheduling Assistant to check if the room is available:
Also, you can view the Free/Busy information by viewing the calendar view of the room mailbox, but the premise is that you must have full access permissions to the room mailbox:
If my reply helps you, please mark it as an answer. Thanks for the understanding.