The database in recovery
Does anybody has other ideas to solve this problem?

Do as error message says, perhaps you connected wrong SQL Instance this time.
Using following query, you can verify whether the database part of AG or not:
select name, IIF(group_database_id IS NULL, 'NO', 'YES') is_joined_AG 
from sys.databases;

select DB_NAME (database_id) mirrored_db
from sys.database_mirroring
where mirroring_guid is not null;