feat: Support `part of` Declarations for Shared Logic in Route Handlers

[loveoverflowdev]

Description

Dart Frog does not support using part of declarations in route files. This limits our ability to share reusable logic across multiple route handlers without duplicating code or resorting to workarounds.

Requirements

• [ ] All CI/CD checks are passing.
• [ ] There is no drop in the test coverage percentage.

Additional Context

No response