fix: resolve failing tests and type errors across api and shared packages

[stooit]

Summary

Fixes all failing tests and type errors in the multi-package TypeScript HTTP API repo. Final state: 22 tests pass, 0 fail; tsc --noEmit clean.

Changes

• Pagination utility (packages/shared/src/utils/pagination.ts): implemented the previously stubbed paginate() (page slicing, total, totalPages, page, pageSize, empty/out-of-range handling) to satisfy the test contract.
• Auth middleware (packages/api/src/middleware/auth.ts): fixed an HTTP-method case-sensitivity bug that caused POST /users not to be treated as a public route; resolved the process type error via tsconfig types.
• Users route (packages/api/src/routes/users.ts): added the missing badRequest import causing a runtime failure for the missing-fields case.
• Shared types (packages/shared/src/types.ts): aligned the User field name to username to match the contract used across both packages and the tests.
• tsconfig.json: configured node/bun types to eliminate Cannot find name 'process' and Cannot find module 'bun:test' errors.

Verification

• bun test → 22 pass / 0 fail
• npx tsc --noEmit → exit 0

Assumptions

• The canonical field name is username (not userName) because the unmodifiable test files reference username; the shared type and source usages were aligned to the tests, which are the contract.
• Type-resolution issues were fixed via tsconfig (using already-available type packages); no new dependencies were added and no test files were modified.