`chown postgres` of a subdirectory not working for a new disk
The permissions on the /mnt/fast_data directory are drwxrwx---, meaning that user main_user and group main_user have full access (read, write, access), but all others have no permissions at all.
You need to chmod o+rx /mnt/fast_data so that its permissions become drwxrwxr-x, giving others the permission to see its contents and access it.