I think the answer you’re looking for has been provided. You can use Anvil App Server, hosted wherever you want, and there will be no changes to the platform beyond those you chose.
Companies like https://a2hosting.com/ offer unmanaged VPS hosting starting at $4.99 per month (I currently have Anvil apps running on a2hosting servers). It takes a few minutes to pip install anvil-app-server and copy the GIT repository for any project you’ve created in an account at anvil.works, and then it runs permanently with the same version of Anvil. It’s extremely simple, fast, and cheap to do (and you can do the same with any framework in any other language…). You don’t have to mess with docker containers, or cloud hosting expenses, and you can even create Anvil projects entirely in code using a text editor, without any involvement with anvil.works whatsoever - if you don’t want/need to use the nice IDE with autocomplete, visual UI builder, data table editor, etc., because your concerns are more heavily weighted towards controlling your environment and tooling. You can make that choice. Nothing is tying you to the anvil.works cloud services whatsoever. Or you can use all the convenience of the anvil.works hosted environment during development (use the classic editor to avoid changes and updates that are being made to the beta editor) then just copy the project GIT repository to your own anvil-app-server for production, and let it run is that untouched state forever.