Hey @Harshad Sadanand Hindlekar
Since you're deploying a zip deploy, make sure that SCM_DO_BUILD_DURING_DEPLOYMENT=true
is set as application setting. Not doing this, the platform more than likely is mounting your zip file as the source which expects all dependencies to configured and the program to be able to run. Also check drop folder to ensure that release.zip does contains the files as you expect. Deployment Center in the Azure Function will also show the incoming file and how gets unzipped or mounted, so you can also check that to make sure the zip has/shows contents.
Having said that, you can refer to Continuously update function app code using Azure Pipelines | Microsoft Learn to compare and contrast against your pipeline.