Hi,
brtools offline backup just stops the database instance, and then it starts the database once the backup gets completed. I doubt if it stops listener process also until and unless someone modified configuration intentionally.
In above logs I could just see database instance shutting down and starting.
Could you please paste error logs where offline backup says that listener is getting down, also paste the logs where it is trying to start default listener and throwing error,
This would help us in to get more details on same and get some direction towards cause of failure.
Cheers !!!
Ashish