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Hello @Aydin Yusifov
To allow an external user to book a meeting room resource directly, the room mailbox must first be configured to process meeting requests from external senders.
This requires an administrator account with at least the Exchange Administrator role. Please run the following commands in Exchange Online PowerShell:
Connect-ExchangeOnline
Set-CalendarProcessing -Identity "Lavender" -ProcessExternalMeetingMessages $true
In the example above, "Lavender" is the display name of the room resource. Please replace it with the appropriate room name if necessary.
Once this configuration has been applied, the external user can create a Teams meeting (or Outlook meeting invitation) and add the room's email address as an attendee/resource. The room mailbox should then process the request in the same way as it does for internal users, subject to the room's booking policies and availability.
Could you please give this a try and let me know the outcome? I look forward to hearing from you.
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