fix: resolve all test failures and type errors across api and shared packages

[stooit]

Summary

• Auth middleware: Fixed case-sensitivity bug where HTTP method comparison used lowercase ("post") but Hono passes uppercase ("POST"), causing public routes to incorrectly return 401
• Users route: Added missing badRequest import and fixed field name from username to match the User type definition
• Shared types: Aligned the User type field name (name → username) to match what both tests and route handlers expect
• Pagination utility: Implemented the paginate<T>() function with proper 1-indexed page slicing, returning { data, page, pageSize, total, totalPages }
• TypeScript config: Added bun-types to resolve process.env typing error in auth middleware

Verification

All 22 tests pass across 4 test files with 37 assertions. Zero TypeScript type errors (tsc --noEmit clean).

Assumptions

• The User type's field should be username (not name) since both tests and route handlers use that name
• Pagination is 1-indexed (page 1 = first page) based on test expectations
• Out-of-range pages return empty data arrays with correct metadata