ci: Migrate to GitHub Actions and reusable workflows, part three (final) (#118)

### Motivation

Following on from #116 and #117, we have now disabled the webhook that
was driving the old CI and updated the branch protection rules to
require the new GitHub Actions based CI checks.

We can now delete the final shims that were keeping the old CI green,
since it is no longer running and complete the migration.

### Modifications

- Delete all Docker bits and scripts used by old CI.

### Result

Migration complete.

### Test Plan

We should be seeing _only_ GitHub Actions checks on this PR and they
should all be passing (apart from the ones that are explicitly
disabled).

Author: simonjbeaumont