ci: type check the docs site

[av1155]

Closes #753

Summary

test-deploy.yml ran only pnpm run build, and the Docusaurus build transpiles TypeScript without checking it. A type error in website/ passed CI silently.

Changes

• test-deploy.yml: run pnpm run typecheck before the build. It is the cheaper of the two, so it fails first.
• test-deploy.yml: trigger on changes to the workflow itself, so this PR exercises the new step rather than deferring proof to the next unrelated docs change.

Testing

Appended a deliberate type error to website/src/pages/index.tsx and ran both scripts against it:

pnpm run typecheck  -> exit 2   src/pages/index.tsx(279,7): error TS2322:
                                Type 'string' is not assignable to type 'number'
pnpm run build      -> exit 0   [SUCCESS] Generated static files in "build".
                                (and printed "not a number" during the build)

The build cannot catch this, which is the gap being closed. The probe was reverted and website/ confirmed clean before committing.

Also checked that typecheck passes from a clean checkout with no generated .docusaurus directory, so it does not depend on running after the build.

Verified against live branch protection that Test docs build is not one of the 11 required checks, and the job name is unchanged, so nothing about the required set moves. The new step is named Type check, but steps do not create check names, so there is no collision with the required Type check (mypy) job.

Type of Change

• CI/CD (ci:)

Checklist

• Issue exists and is linked above with Closes #N
• Linked issue has exactly one type:* and one priority:* label
• Linked issue has at most one phase:* label (or none when not roadmap work)
• Branch name matches issue scope
• Tests added/updated for all changes — N/A, CI config
• No secrets or sensitive data committed
• Scope check: CI coverage only, no runtime change