No root-level npm script to typecheck all workspaces in one command

[vjuliaife]

Description:
CONTRIBUTING.md instructs contributors to run typecheck separately per workspace (npm run typecheck --workspace=apps/web, plus manual tsc --noEmit invocations for apps/api via lint-staged config) with no single root command. Every other check (build, lint via --workspaces --if-present) has a root aggregate except typecheck, forcing contributors to remember three separate commands before pushing.

Acceptance Criteria:

• Add a root "typecheck": "npm run typecheck --workspaces --if-present" script (and ensure apps/api exposes a matching per-workspace typecheck script, since it currently only typechecks via lint-staged)
• Confirm the aggregate script fails non-zero if any workspace fails
• Update CONTRIBUTING.md's pre-push checklist to reference the single command
• Wire it into CI where it duplicates per-app typecheck steps, if applicable

Relevant Files:

• package.json — no aggregate "typecheck" script exists
• apps/api/package.json — has no dedicated typecheck script; tsc --noEmit only runs via lint-staged
• CONTRIBUTING.md — documents three separate typecheck invocations instead of one command