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

[stooit]

Summary

Fixes all 9 failing tests and 14 tsc --noEmit errors in the api/shared multi-package repo. Baseline was 9 fail / 14 type errors → now 22 pass / 0 fail and tsc clean.

Fixes

• Pagination (shared): implemented paginate() (was a not implemented stub) — page slicing, total, totalPages, page/pageSize, empty/out-of-range handling. Also guards non-finite page/size with Number.isFinite (prevents NaN→null serialization and an Infinity-driven unbounded-response path).
• Shared types: reconciled the User field name to username consistently across both packages (tests expected the shared type's name; source now matches).
• Route handler (api): added the missing badRequest import in routes/users.ts — fixes POST /users 400-on-missing-fields.
• Auth middleware (api): fixed a case-sensitive HTTP-method comparison so public routes (e.g. POST /users) are recognized regardless of method casing.
• tsconfig: referenced already-installed bun types so process / bun:test resolve. No new dependencies added.

Verification

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

Assumptions

• Where tests and source disagreed on the field name, source was changed to match the tests / shared User type (per instructions not to modify tests).
• tsconfig types were wired to packages already present in node_modules; nothing was installed.

Notes

• No test files modified; no dependencies added.