There are configurations available in ADF to generate and save log files to a datalake container:

Refer: https://learn.microsoft.com/en-us/azure/data-factory/copy-activity-log?tabs=data-factory

How to capture the each activity logs in the table in adf:

Refer: https://learn.microsoft.com/en-us/answers/questions/1922633/how-to-capture-the-each-activity-logs-in-the-table