UPDATE
I've documented my problem and solution in much more detail here »
I had been trying to deploy my script as a Cloud Run Service. I should've tried deploying it as a Cloud Run Job. The difference is that cloud run services require your script to listen for a port. jobs do not.

Confusingly, you cannot deploy a cloud run job directly from Artifact Registry. You have to start from the cloud run dashboard.
Answer from Ben on Stack OverflowAutomating Python with Google Cloud
docker - How to run a "hello world" python script with Google Cloud Run - Stack Overflow
What's the best way to run python scripts on the cloud to process Google Sheets data?
Trying to trigger Cloud Run Job from python/django and not wait for the result
Videos
I just published a tutorial series on how to automate a Python script in Google Cloud using Cloud Functions and/or Cloud Run. Feedback would be great. Thanks!
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Automating Python with Google Cloud
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Automating Python with Google Cloud Functions
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Automating Python with Google Cloud Run
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» pip install google-cloud-run
UPDATE
I've documented my problem and solution in much more detail here »
I had been trying to deploy my script as a Cloud Run Service. I should've tried deploying it as a Cloud Run Job. The difference is that cloud run services require your script to listen for a port. jobs do not.

Confusingly, you cannot deploy a cloud run job directly from Artifact Registry. You have to start from the cloud run dashboard.
Your Flask application should be something like below:
import os
from flask import Flask
app = Flask(__name__)
@app.route("/")
def hello_world():
return "Hello World!"
if __name__ == "__main__":
app.run(debug=True, host="0.0.0.0", port=int(os.environ.get("PORT", 8080)))
See this official documentation for step by step instruction: Deploy a Python service to Cloud Run
There is a plugin called: Cloud Code IDE plugin which makes the test and deployment easy. I am using it for VS code, once the initial setups and permissions are taken care, few clicks, you will be able to run locally, debug and deploy Cloud run services from your local instance.