Add CI workflow to check mkdocs build on PRs

[Copilot]

The docs site build (uv run mkdocs build) has no CI gate on PRs to main. The existing deploy_site.yml only runs on the publish branch, so Python source changes or dependency updates that break the docs build go undetected until deploy time.

Adds .github/workflows/docs_build_check.yml:

• Triggers on pushes and PRs to main (same scope as python-app.yml)
• Runs uv sync --no-dev --frozen — mkdocs and plugins are main deps, not dev; --frozen catches lockfile drift
• Runs mkdocs build --clean matching the production build command in deploy_site.yml

Original prompt

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This section details on the original issue you should resolve

<issue_title>Missing docs build check</issue_title>
<issue_description>We have a python build check for tests, but not for mkdocs and other uv run programs.

Some merge commits can break uv run mkdocs and possibly other programs.

We should have more build tests to cover these.</issue_description>

<agent_instructions>See the existing .github/workflows/ files. Work to create more build tests for the static site.</agent_instructions>

Comments on the Issue (you are @copilot in this section)

• Fixes Missing docs build check #1085

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Pull request overview

Adds a GitHub Actions CI gate to ensure the MkDocs site builds successfully on PRs and pushes to main, catching documentation build breakages earlier than the publish-branch deployment workflow.

Changes:

• Add a new workflow that runs on push and pull_request events targeting main.
• Install locked, non-dev dependencies via uv sync --no-dev --frozen.
• Build the documentation with uv run mkdocs build --clean (matching the deploy workflow).

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