Fix API integration: proxy via Angular, date format, root redirect

- Point API_BASE_URL to localhost:4200 (Angular's dev proxy) which
  correctly forwards to flights.test.aeroflot.ru with proper headers
- Convert URL date format (yyyyMMdd) to API format (yyyy-MM-ddT00:00:00)
  matching Angular's ApiFormatterService behavior
- Add standalone api-proxy.mjs script for running without Angular
- Root page redirect uses both loader and client-side navigate
- SignalR hub URL points to platform.yc.webzavod.ru/tracker/hub
- Remove broken server/modern-js.server.ts (proxy handled externally)

package.json

@@ -21,7 +21,9 @@
     "typecheck": "tsc --noEmit",
     "bundle-size": "node scripts/ci/bundle-size-gate.mjs",
     "check-coverage": "node scripts/ci/check-coverage-delta.mjs",
-    "test:e2e": "playwright test"
+    "test:e2e": "playwright test",
+    "proxy": "node scripts/api-proxy.mjs",
+    "dev:full": "node scripts/api-proxy.mjs & pnpm dev"
   },
   "dependencies": {
     "@microsoft/signalr": "^10.0.0",
@@ -67,6 +69,7 @@
     "eslint-plugin-boundaries": "^5.0.0",
     "eslint-plugin-unused-imports": "^4.0.0",
     "fast-check": "^4.6.0",
+    "http-proxy-middleware": "^3.0.5",
     "jsdom": "^29.0.2",
     "react-test-renderer": "^19.2.5",
     "sass": "^1.99.0",