fix: resolve all failing tests and type errors

[stooit]

Summary

• Auth middleware: Fixed case-sensitivity bug where publicMethods used lowercase "post" but HTTP methods arrive as uppercase "POST", causing authenticated routes to reject valid public requests
• Users route: Added missing badRequest import and fixed field name mismatch between request body (username) and User type (name)
• Pagination utility: Implemented the paginate<T>() function that was previously a stub throwing "not implemented"
• TypeScript config: Added bun-types to tsconfig.json compilerOptions.types to resolve bun:test module and process global type errors

Verification

All 22 tests pass, 0 type errors:

bun test → 22 pass, 0 fail, 37 expect() calls
npx tsc --noEmit → clean

Files Changed

• packages/api/src/middleware/auth.ts — uppercase method in publicMethods, removed bare process usage
• packages/api/src/routes/users.ts — added import, mapped username → name
• packages/shared/src/types.ts — ensured User type field consistency
• packages/shared/src/utils/pagination.ts — implemented paginate function
• tsconfig.json — added bun-types for type resolution