Move routes to app router route handlers

[perkinsjr]

We currently serve tRPC, Vercel, Plain and webhooks through the legacy pages api we should move them to app router.

There isn't much reason anymore since tRPC does support app router fully.

The migration should be tested fully from end to end:

1. All tRPC routes
2. Clerk webhooks, Stripe webhooks
3. Plain support requests
4. Vercel integration

Clerk will and Stripe will require changes to the core code to use the new headers API but the business logic can stay the same.

[linear]

ENG-1328 Move routes to app router route handlers

[chronark]

Would be sensible to leave clerk out for now, until we have decided on whether we move to workos or not