Following up on #6532
Split from #6525

This PR follows up on #6532 and migrates assertions in the following types of tests to TSTyche:

register.test-d.ts
reply.test-d.ts
request.test-d.ts
route.test-d.ts
schema.test-d.ts
serverFactory.test-d.ts
type-provider.test-d.ts
using.test-d.ts

For the first part of migration see #6726. Hopefully, a smaller PR makes it easier to review the changes.

Changes

A few notes on the changes made:

• In tsd assertions, the expected value comes first (differently from JavaScript assertions), so I had to swap expected and actual like here:

  - expectType<FastifyBaseLogger>(fastify().log)
  + expect(fastify().log).type.toBe<FastifyBaseLogger>()

• When possible, I used a stricter .toBe() instead of .toBeAssignableTo() (assignability can be assumed)
• Where possible, I replaced @ts-expect-error with .not.toBeCallableWith() and .not.toHaveProperty() (improves readability)
• I have sorted imports manually for consistency

Checklist

• run npm run test && npm run benchmark --if-present
• tests and/or benchmarks are included
• documentation is changed or added
• commit message and code follows the Developer's Certification of Origin
  and the Code of conduct