## Problem
We call `check-build-tools-image` twice for each workflow whenever we
use it, along with `build-build-tools-image`, once as a workflow itself,
and the second time from `build-build-tools-image`. This is not
necessary.
## Summary of changes
- Inline `check-build-tools-image` into `build-build-tools-image`
- Remove separate `check-build-tools-image` workflow