Hi,
step 1:
Try to use Log to table + Include step output in history
This will log all the full message to the job table
Step 2:
If you need to out to file you can do it using Azure Logic Apps and pull the information from the table to a file in the blob for example: https://learn.microsoft.com/en-us/azure/connectors/connectors-create-api-sqlazure
note: I did not try this option for jobs yet, but in first glance it seems like an option.
Note! If you will open a suggestion to support this feature in managed instance using blob for example to store the file, then I will vote it: https://feedback.azure.com/forums/908035-sql-server