fix: make all tests pass and eliminate type errors

[stooit]

Summary

• auth middleware: public-method list used lowercase "post"; c.req.method is uppercase so POST was wrongly rejected. Now "POST", compared case-insensitively.
• users route: badRequest was used but not imported (ReferenceError → 500 instead of 400).
• shared types: User.userName renamed to username to match all consumers.
• pagination: implemented paginate() (1-indexed pages, Math.ceil totalPages, empty data for out-of-range pages).
• tsconfig: added "types": ["bun-types"] (already a devDependency) so tsc resolves bun:test and process.

Verification

• bun test: 22 pass, 0 fail
• bunx tsc --noEmit: exit 0

Assumptions / notes

• tsc isn't on PATH here; ran via bunx tsc.
• POST being public is the documented intent per the middleware docblock and tests; worth revisiting against authentication policy before production.
• No test files modified, no dependencies added.