ci: Remove CI builder (#13965)

We were using both Docker-based CI builder images as well as self-hosted runner images with software preinstalled. This was causing discrepancies between software versions when things were updated. Furthermore, changing `mise.toml` required a manual rebuild of the CI builder image for changes to take effect.

This PR updates the CI pipeline to use Mise to install all tool necessary to run the monorepo. Preinstalled tools have been removed from the self-hosted runners, and all Docker images in the pipeline have been replaced with a simple `cimg/base` image.