Yes - same as with the original script, upgrades would require more manual steps than just updating the version in the Compose file. This is how it’s typically done.
There are ways to automate this. Docker Hub used to have a feature for automatic rebuilds when base images had changed, but AFAIK this feature was removed some years ago. Now it’s a matter of setting up a CI with periodically (nightly or weekly) scheduled pipelines, but it’s not a trivial matter.
Semi-automation can be achieved by using build-time arguments. I’m at my computer now, so here’s a revised process:
First, a bunch of manual commands that would allow us to write a patch. I’ll use those crude sed statements - just because they work today, but YMMV.
And finally, create a file called .dockerignore that contains only one line that would say build.sh. That’s just minor cosmetic touch saying that our build.sh is not meant to be a part of the build context. If everything is correct, there should be now 4 files in the directory: .dockerignore, build.sh, change-limits.patch and Dockerfile.
Now when you run build.sh it will automatically find the latest version and build you a custom image tagged as e.g. my-mastodon:v4.1.3, which you can use in your Compose file. For a distributed system like Docker Swarm, Nomad or Kubernetes you’ll want to tweak this script a little to use some registry (your-registry.example.org/your/mastodon:v4.1.3) and possibly even apply changes further (e.g. docker service update --image …).
Mutable tags like latest can become confusing or even problematic (e.g. if you’ll want to downgrade it’s best to have previous version image readily available for some time - even if the build process is reproducible), so I would really recommend to use explicit version number tags.