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

[stooit]

Summary

Fixes all failing tests (now 22/22 passing) and all tsc --noEmit type errors across the api and shared packages. Bugs spanned both packages as anticipated.

Fixes

• Auth middleware (packages/api/src/middleware/auth.ts): the public-method allow-list contained lowercase "post", but Hono normalises HTTP methods to uppercase per RFC 7231, so POST /users never matched and was rejected with 401. Corrected to "POST".
• Shared types (packages/shared/src/types.ts): User.userName was inconsistent with the db layer, route handlers, and test expectations, all of which use username. Reconciled the type to username so the field name is consistent across both packages.
• Route handler (packages/api/src/routes/users.ts): added the missing badRequest import that caused a runtime/type failure.
• Pagination utility (packages/shared/src/utils/pagination.ts): implemented the previously-stubbed function — 1-indexed pages, correct partial last page, empty input (totalPages: 0, no NaN), and out-of-range pages (returns empty data without crashing).
• tsconfig (tsconfig.json): added bun-types and the @e2e/shared path alias to resolve bun:test, the process global, and cross-package imports. No new dependencies added.

Verification

• bun test -> 22 pass, 0 fail
• tsc --noEmit -> clean (exit 0)

Constraints honoured

• No test files modified
• No new dependencies added
• Changes are minimal and limited to what the tests require

Assumptions

• Where a test and source disagreed on a field name, the test was treated as authoritative (username over userName).
• The bun-types / @e2e/shared tsconfig entries rely on packages already present in node_modules; no additions to package.json or the lockfile were made.