Public Docker image quality-of-life improvements

[!NOTE]
Moved from rstudio/platform-team#188

This came out of conversations with @colearendt and @bschwedler. Essentially, there are some things we'd like to improve about our public Docker images -- for the products especially but also their upstream base images -- but that are scattered across various people's heads or some isolated issues.

Items we've discussed as potential improvements:

• Image rebuilds automatically triggered by updates to the base image. Ideally we'd like a holistic update cycle so it's clear how changes to r-docker base images and even r-build OS packages trigger updates up the stack. This should also catch security patches to the OS base images we use.

• More efficient continuous integration. Currently CI for rstudio-docker-products (which runs on every commit and PR) takes about an hour, which really cuts into iteration time. Most of this is due to rebuilding all images even when a commit only touches one of them. Cole has some work in progress to improve this.

• More layer optimisation (and, related, "as small as possible" images). We can potentially use tools like dive for analysis here.

• Image signing (see #183) and signature verification of upstream components (GPG for packages, maybe Sigstore for base images).

• Whether we can produce minimalist/distroless builds for Connect and Package Manager (for dramatically smaller images and improved image security).

• Whether r-docker should be moved from Jenkins to GitHub Actions. It's a public project, so that seems like a reasonable choice and is consistent with rstudio-docker-products.

This is an umbrella issue rather than a single implementation task. Start by reviewing the unchecked items, especially the linked image-signing issue #183, and inspect the existing CI and image-build workflows in rstudio-docker-products and r-docker. Done requires narrowing one improvement into a concrete plan with defined image, workflow, or security outcomes.