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 workspace. bun test now passes 22/22 and npx tsc --noEmit is clean.

Changes

• shared/types.ts — renamed User.userName → username to match the route handlers, db seed data, and tests (field name was inconsistent between packages).
• shared/utils/pagination.ts — implemented the paginate() stub (previously threw "not implemented"). 1-indexed pages: data = items.slice((page-1)*size, ...), total, totalPages = ceil(total/size) (0 when empty), returns empty data for out-of-range pages.
• api/middleware/auth.ts — fixed a case-sensitivity bug: the public-method allow-list contained lowercase 'post' while Hono's c.req.method is uppercase, so POST /users was wrongly requiring a token.
• api/routes/users.ts — added the missing badRequest import from ../lib/errors (runtime failure on validation path).
• tsconfig.json — added bun-types so bun:test and node globals (process) resolve. No new dependencies (bun-types already installed).

Verification

• bun test → 22 pass, 0 fail
• npx tsc --noEmit → clean

Constraints honoured

• No test files modified
• No new dependencies added
• Only the changes the tests required

Assumptions

• Correct field spelling is username (lowercase n) — tests, db seed, and route logic all use it; only the shared type declared userName.
• paginate pages are 1-indexed, per the pagination test contract.