ci: gate packages/types on tsc

[lilyshen0722]

Stacked on #826 — base is that branch, not main, because #826 is the only other open PR touching tests.yml and this lands in the adjacent hunk. Merge #826 first and this rebases to nothing.

packages/types defines typecheck: tsc --noEmit and nothing has ever invoked it — the same defined-but-uninvoked shape #826 fixes for the frontend. @ux-lead found it; this gates it.

It costs no install

The package has zero dependencies and zero external imports, so it typechecks with the compiler the backend step already installed:

- name: Shared types TypeScript check
  run: |
    cd packages/types
    ../../backend/node_modules/.bin/tsc --noEmit -p tsconfig.json

That's a correction to the framing it was handed to me with ("a two-line add whose only cost is an install step") — there is no install step. Verified: deps: {}, devDeps: {}, and no non-relative import anywhere in src/.

It is green today, which is the only moment a gate is free.

Mutation-checked

A gate that cannot go red is decoration, so:

state	result
clean	exit 0
export const __mutationProbe: number = "not a number" in src/user.ts	TS2322, exit 2
probe reverted	exit 0, git status clean

Workflow YAML re-parsed after the edit; step lands after both existing typechecks and before the test steps.

packages/commonly-apps is deliberately NOT here

It has the identical uninvoked tsc:check, but it needs @types/node and this job never npm cis it, so gating it means adding an install step — a different change with a different cost. Running it as-is yields TS2688 cannot find type definition file for 'node', which is an environment gap, not a finding. Its real state is unknown, not assumed green. Flagging rather than silently scoping it out.

Not verified

Any follow-up that adds the packages/* install + commonly-apps step touches .github/workflows/ again and needs the workflow-scoped token — same constraint this push had.

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