fix: harden Next.js pages against API startup errors

[user040131]

Summary

• add retry and timeout handling in the shared web API client so initial API startup races do not immediately crash SSR pages
• add a shared page error state and route error boundary so unhandled issues render user-friendly fallback UI instead of a raw Next.js overlay
• rewrite the main page surfaces with clean Korean copy and per-page try/catch handling, and update Next config to the current typedRoutes setting

Verification

• npx pnpm --filter @finance-helper/web exec tsc --noEmit
• checked http://localhost:3000/dashboard, /events, /themes, /replay, /evaluation, /admin
  • all returned 200

Related

• Closes [v0.5.6] Next.js 프런트 전체 오류 처리 및 렌더링 안정성 점검 #24
• Stacked on top of perf: improve sidebar navigation responsiveness #23