If the SQL Backup Agent Windows Service is having issues with accessing files across the domain. the below test will confirm whether the account has permissions to the file in question.
Run the following query in SSMS with the SQL Backup Server Components installed to ensure that the SQL Backup Agent has permissions to the network location (making sure to replace <network location> with the unc path to the network location):
EXECUTE master..sqbutility 999, 'RWE', '<network location>'
If this is successful and the SQL Backup Agent service has read (R), write (W), and execute (E) permissions, the query will return:
If there is a problem, the query will return a value of 0, followed by a message, for example:
<SQBUTILITYRESULT>:0:Folder does not exist :
If it returns 0, please take a look at the following documentation and ensure your SQL Backup Agent account has the necessary permissions: