[codex] Add TypeScript starter app smoke tests

[rlippmann]

What changed

This adds small, variant-local smoke tests for the split TypeScript starter apps:

• typescript/starter_apps/node/basic
• typescript/starter_apps/node/with_drafter
• typescript/starter_apps/nextjs/basic
• typescript/starter_apps/nextjs/with_drafter

The tests stay focused on starter-app behavior rather than re-testing core engine semantics.

Why

We split the starter apps into basic and with_drafter variants, and these examples need lightweight coverage that proves the starter wiring still behaves as documented without depending on the older monolithic test shape.

Behavior covered

• missing sessionId / input returns a validation error
• clarify responses do not produce downstream request payload/output
• repeated sessionId preserves checkpoint behavior across turns
• history replay works when no checkpoint is saved
• with_drafter variants additionally cover:
  • directive-adjacent input becoming compiler input
  • pending clarification bypassing drafting
  • unknown or unsafe drafter output falling back to raw input

Implementation notes

• Node starters now export a small request handler for test use so smoke tests can run without binding a local port.
• Next.js starter tests import the route handler directly.
• Each starter app now has its own minimal test script.

Validation

• typescript/starter_apps/node/basic: npm test, npm run typecheck
• typescript/starter_apps/node/with_drafter: npm test, npm run typecheck
• typescript/starter_apps/nextjs/basic: npm test, npm run typecheck, npm run build
• typescript/starter_apps/nextjs/with_drafter: npm test, npm run typecheck, npm run build

One temporary typecheck failure in nextjs/with_drafter was resolved by rerunning after next build generated .next/types; the final rerun passed cleanly.