fix: resolve all test failures and type errors

[stooit]

Summary

Fixes all failing tests (22 tests now pass) and eliminates all TypeScript type errors across the api and shared packages.

Changes

• Auth middleware (packages/api/src/middleware/auth.ts) — Fixed case-sensitivity bug in HTTP method comparison. The middleware was comparing request methods without normalizing case, causing POST requests to be incorrectly blocked by auth.
• Shared types (packages/shared/src/types.ts) — Renamed userName → username and emailAddress → email to match the field names used throughout the API routes and tests.
• Users route (packages/api/src/routes/users.ts) — Added missing badRequest import from the errors library.
• Pagination utility (packages/shared/src/utils/pagination.ts) — Implemented the paginate function (was previously a stub throwing "not implemented").
• TypeScript config (tsconfig.json) — Added bun-types to compiler options for proper process type resolution.

Verification

bun test → 22 pass, 0 fail, 37 expect() calls
npx tsc --noEmit → no errors

Assumptions

• No test files were modified
• No new dependencies were added
• Field renames in the shared User type are safe since all consumers (routes + tests) use the new names