What would you recommend I do instead? Deploying a Docker container on Cloud Run sorta seemed like the logical way to deploy my micro app.

Also for more context, this was the app in question (now moved to streamlit cloud): https://jreadability-demo.streamlit.app/

Skip all that jazz and write some php like it's 1998 and pay 5 bucks a month for Hostens or the equivalent... Well, that's the opposite costing side of the spectrum from serverless containerized dynamic lang runtime and a zillion paid services as a backend.

Your standard web hosting services, or a cheap VPS are great options.

The whole 'cloud serverless buzzword-here' thing is ridiculous for most use cases.

Heck you can serve quite a few static req/s on a $2 ESP32 microcontroller.