How can we push AEM logs to Microsoft Application insight automatically

Hi, 

Yes, you could build a custom process to push those AEM logs to whatever you need. You can use the Adobe I/O Cli to download the logs and do with them what you need. Please check these resources: 

https://developer.adobe.com/runtime/docs/guides/tools/cli_install/

https://experienceleague.adobe.com/en/docs/experience-manager-cloud-service/content/implementing/using-cloud-manager/manage-logs#logs-through-api

https://github.com/adobe/aio-cli-plugin-cloudmanager?tab=readme-ov-file#aio-cloudmanagerenvironmentdownload-logs-environmentid-service-name-days

Hope this helps