Refactor remaining endpoints to FastAPI APIRouter

[korikuzma]

Feature description

I think we should refactor the REST API to consistently use FastAPI APIRouter, following the existing vcf router

Use case

Will improve readability, maintainability, + follow FastAPI best practices

Acceptance Criteria

• VCF routes stay the same
• Remaining routes are split into separate routers (vrs, search, general)
• No changes to endpoint paths, behavior, or responses
• Tests continue to pass

Proposed solution

No response

Alternatives considered

No response

Implementation details

No response

Potential Impact

No response

Additional context

No response

Contribution

None

[jsstevenson]

This gets a 👍 from me, but I think we should first do a review of the endpoints themselves and double-check that we don't have any planned changes or additions, then we can divide them up into modules