[CI] Add clang-tidy to UBTI GitHub Action

The Unified Build, Test, and Install reusable GitHub actions workflow is becoming the main workhorse for CI. Currently, unlike the "Build and Test" action, this does not support running clang-tidy. Extend this so that clang-tidy can be run, ideally optionally.

Ideally, this is handled via an additional input to the `workflow_call`. I _think_ we get up to 100 inputs for a `workflow_call`, while a `workflow_dispatch` is limited to 10. (Or so the LLMs claim...) It is fine if this is not easily accessible via the `workflow_call`.

Locate the reusable Unified Build, Test, and Install workflow and compare its inputs and clang-tidy handling with the “Build and Test” action. Trace the workflow_call interface and verify that an optional setting enables clang-tidy without changing default behavior; done means the workflow supports an optional clang-tidy run.

Written by the indexing model from the issue text.