Move type, lint, and format checks into their own workflow (#2263)

## Description

Moves the `checks` job (lockfile drift, types, lint, format) out of
`unit.yml` into a new `checks.yml` workflow. The job itself is
unchanged.

This sets up the next PR, which skips unit tests and the Docker test
build for docs-only changes. Formatting has to keep running on those PRs
because it checks markdown, so it needs its own workflow without the
path filter.

## Validation

- `pnpm check:format` passes on the workflow files.
- This PR's own run shows a separate Checks workflow alongside Unit
Tests.

## Related Issues

None.

### Check List

- [x] I confirm that my contribution is made under the terms of the
Apache 2.0 license.
- [x] I have verified `pnpm checks` passes with no errors.
- [x] I have verified `pnpm test` passes with no failures.
- [ ] I have covered new added functionality with unit tests if
necessary.
- [ ] I have updated documentation if necessary.

Author: kmcginnes