Your conclusions are correct, and this is a useful writeup for anyone else building outside the Node.js/Remix ecosystem.
The shopify.app.toml file is required for all apps (embedded or not), and you do need to run shopify app deploy via the CLI to register your compliance webhook endpoints with Shopify. The CLI deploys your app configuration (webhook subscriptions, scopes, URLs) to Shopify’s servers. It doesn’t build or run your app, so it works regardless of your backend language. A similar thread for a Java/Spring Boot backend confirmed the same thing.
The Azure Functions routing workaround you documented is very helpful. The compliance webhook docs and app configuration reference cover the TOML setup, but nothing there addresses the Azure Functions routing specifics, so having this here will save others time. Thanks for posting @Randal_B!