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

[stooit]

Summary

Fixes all 9 failing tests and all tsc --noEmit type errors in the Bun/Hono monorepo. Final state: 22 pass / 0 fail, npx tsc --noEmit clean (exit 0).

Changes

• shared/src/utils/pagination.ts — implemented paginate<T>() (was a throw new Error("not implemented") stub), satisfying the full PaginatedResponse contract: page slicing, partial last page, total/totalPages, page/pageSize echo, and empty/out-of-range pages returning empty data.
• shared/src/types.ts — renamed User.userName → username to reconcile the inconsistency between the shared type, the users route, and the tests.
• api/src/routes/users.ts — imported badRequest (previously used but unimported → ReferenceError on POST /users); aligned field to username.
• api/src/middleware/auth.ts — fixed the public-route allow-list: HTTP method is now normalised (case-insensitive) so POST /users is correctly treated as public. Resolved the process type error via tsconfig.
• tsconfig.json — added bun-types to compilerOptions.types (resolves bun:test module + process type errors). No new dependencies added.

Verification

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

Constraints honoured

• No test files modified.
• No new dependencies added.
• Fixed only what the tests/type-checker required.

Notes / assumptions

• Canonical field name resolved to username (lowercase) because that is what the read-only tests and route body expect.
• A review flagged optional hardening for paginate() on non-finite / zero size inputs. Those paths are not exercised by any test and paginate() is not yet wired to a route, so they were left out of scope per "fix only what the tests require." Worth a follow-up if paginate is later bound to request query params.

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