Azure SQL Database - Error Starting Extended Events Session
So the answer was to check every database in the elastic pool for extended event sessions and then stop and delete the few running ones I found. After that a retry worked.
The hint was in the error message :-


Check sys.dm_xe_database_sessions for active sessions that can be stopped or altered.


I'd like to claim I wrote some smart powershell to iterate through every database - but actually I did a LOT of clicking in SSMS (Powershell next time).