feat: add a health check endpoint

[0c-coder]

add a health check endpoint

Step	Agent	Model
Generate	Claude Code	sonnet (subscription)
Review	Codex CLI	codex-1 (subscription)
Validate	Claude Code	sonnet (subscription)

 apps/web/package.json                     |  7 ++-
 apps/web/src/app/api/health/route.test.ts | 81 +++++++++++++++++++++++++++++++
 apps/web/src/app/api/health/route.ts      | 50 +++++++++++++++++--
 apps/web/vitest.config.ts                 | 14 ++++++
 4 files changed, 145 insertions(+), 7 deletions(-)

agent-pipeline • 20260318-154228