Publish Docker image

The clean building of the Docker image takes quite a while (as it has to perform a complete build of the application, preferably in Release mode), so it'd be great for us to publish the image, presumably to Dockerhub, so that consumers can simply pull and run the image.

Here's the workflow we have to publish the image for the main Badge Server that should serve as a useful reference

https://github.com/badges/shields/blob/master/.github/workflows/publish-docker-next.yml

To control the build mode, be sure the docker build arg `CARGO_BUILD_MODE` is set to `release`

Start by reviewing the referenced .github/workflows/publish-docker-next.yml workflow in the Shields repository and compare it with Squint’s Docker build setup. Ensure the docker build arg CARGO_BUILD_MODE is set to release, then verify that consumers can pull and run the published image from the chosen registry.

Written by the indexing model from the issue text.