## 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
## Problem
The Merge queue doesn't work because it expects certain jobs, which we
don't have in the `pre-merge-checks` workflow.
But it turns out we can just create jobs/checks with the same names in
any workflow that we run.
## Summary of changes
- Add `conclusion` jobs
- Create `neon-cloud-e2e` status check
- Add a bunch of `if`s to handle cases with no relevant changes found
and prepare the workflow to run rust checks in the future
- List the workflow in `report-workflow-stats` to collect stats about it
