#523 - TypeScript hardening for runtime-critical path

Parent: #523

## Objective
Increase type safety where failures are most costly by removing `@ts-nocheck` and tightening types in bootstrap/router/auth entry paths.

## In scope
- Prioritize: `src/index.ts`, `src/router/index.ts`, `src/libs/authmware.ts` (and directly related helpers)
- Remove `@ts-nocheck` in targeted files
- Add/adjust types for request context, auth payloads, and shared utilities

## Acceptance criteria
- Target files compile without `@ts-nocheck`
- No behavior regressions in auth + route bootstrap
- Unit/integration tests pass for touched paths
- New/changed code avoids broad `any` where practical

## Notes
Work in small PRs to keep review manageable.