feat(FN-281): add payment_success and payment_failed PostHog events (+1 more)

Commits merged:
- fix(FN-281): make result search param truly optional to fix typecheck
- feat(FN-281): add payment_success and payment_failed PostHog events

Files changed:
apps/api/package.json                              |    1 +
 apps/api/src/app.module.ts                         |    2 +
 apps/api/src/payments/payments.service.spec.ts     |   99 +-
 apps/api/src/payments/payments.service.ts          |   40 +
 apps/api/src/posthog/posthog.module.ts             |    9 +
 apps/api/src/posthog/posthog.service.ts            |   64 ++
 .../web/src/components/payment/payment-content.tsx |   24 +-
 apps/web/src/routeTree.gen.ts                      | 1110 ++++++++++----------
 apps/web/src/routes/dashboard/subscription/pay.tsx |   24 +-
 packages/config/src/index.ts                       |    4 +
 pnpm-lock.yaml                                     |   30 +
 11 files changed, 827 insertions(+), 580 deletions(-)

Fusion-Task-Id: FN-281

apps/api/package.json

@@ -60,6 +60,7 @@
     "ioredis": "^5.4.0",
     "openai": "^6.37.0",
     "postgres": "^3.4.0",
+    "posthog-node": "^5.34.1",
     "reflect-metadata": "^0.2.2",
     "rxjs": "^7.8.0",
     "undici": "^7.22.0",