You should not use App Insights for this.
You need to configure your ADF instance to send its logs to log analytics workspace. Then your ADF logs are available on AzureDiagnostics table or in ADF-specific tables.
ref: https://learn.microsoft.com/en-us/azure/data-factory/monitor-configure-diagnostics
Edit:
- Make sure that you use secure input and secure output settings on the actions that pass/use sensitive data
-
secure output
can be also used to mask output of stored proc/web/script/lookup calls. On some cases those activities generate so much log that Output field on log analytics contains only errors message and log analytics with other content will be impossible.