ci: add types testing with `tstyche` (#9803)

As proposed here
https://github.com/payloadcms/payload/pull/9782#issuecomment-2522090135
with additional testing of our types we can be more sure that we don't
break them between updates.

This PR already adds types testing for most Local API methods
https://github.com/payloadcms/payload/blob/6beb921c2e232ab4edfa38c480af40a1bec1106e/test/types/types.spec.ts
but new tests for types can be easily added, either to that same file or
you can create `types.spec.ts` in any other test folder.

The new test folder uses `strict: true` to ensure our types do not break
with it.

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Co-authored-by: Tom Mrazauskas <tom@mrazauskas.de>