Cherry-pick updates of CI check scripts from qualtran

**Description of the issue**

Sync useful changes in the check/something scripts here and in Qualtran after the fork.

- [ ] https://github.com/quantumlib/Qualtran/pull/1009

**Cirq version**

main at e4b6ab2f1f01b3c2d06456eb7244430e691474ef