Attempt to cache docker images in CI

[alexcrichton]

Linux package servers have been particularly flaky today so I've re-investigated how to maybe cache everything. The idea here is that we use the "officially recommended" way of caching builds of docker images on github actions, notably using the github actions cache. The way this is configured is that some extra steps happen on github which populate the github actions cache and local docker daemon such that when the actual build happens, totally independently of these github actions steps, it just so happens to get cache hits. This is done to ensure that if we make a mistake here it doesn't result in stale builds, just slower builds.

The overall hope here is that by using the github actions cache for docker images we can hit package installation less than we currently do. The hope is that all the images fit within the github actions cache. I think they do but it's pretty noisy and each build generates new entries so I'm not entirely sure what's happening. Local testing shows that reruns do indeed proceed faster and don't hit apt-get for example, though.

This doesn't entirely insulate us from issues with apt-get because runs will still use apt-get externally from docker, such as just installing a few extra packages. I don't know how to make those more robust, but hopefully we can at least reduce some flakiness by caching some things.