I have been building and setting up some new Windows Server 2022 RDS farms recently and ran in to an issue when adding a second RDS connect broker after configuring High Availability.
The server would install the broker role and then fail to configure. This would return the below error.
The list of joined nodes could not be retrieved on servername. Privilege not held.

I was also getting EventID 32814 and 4119 in the Microsoft-Windows-Rdms-UI/Admin event logs.
I enabled the debug logging also but this only returned the same error as where showing in the event logs.
To fix the issue I had to logon to the server I was trying to add as a secondary broker and remove the below registry value.
Make sure to backup the registry key before deleting any values.
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Tssdis\Parameters\DBConnString

After deleting, I had to remove the RDS broker roles from the server that failed to install and reboot.
Then I tried the install again and this time it completed without issue.
This seems to be a bug in Windows Server 2022.