There are several ways to deploy Docker images on Microsoft Azure.
My favorite one is Azure App Service/Web Application for Containers.
This is the closest to Google Cloud Run.

Start from my Makefile for Azure.

# Every few hours
$ make one_time_setup
# Deploy to Azure Web Apps (AWA)
$ make docker_awa_deploy
# You can see the logs from the deployment via
$ docker_awa_stream_logs

Note:

  1. Microsoft Azure, in general, is less reliable than AWS or Google Cloud.
  2. On Microsoft’s Azure, sometimes, changes take minutes to propagate! And the stale UI entries are common as well.