feat(web): integrate TanStack React Router for client-side routing

Replace state-based screen navigation with proper URL-based routing. This includes:
- New router configuration with routes for sessions, machines, and spawn pages
- App context provider to share API and token across the app
- useAppGoBack hook for handling browser and Telegram back navigation
- Refactored App component to render outlet and use router hooks
- Memory history for Telegram app, browser history for web

web/src/hooks/useAppGoBack.ts

@@ -0,0 +1,30 @@
+import { useCallback } from 'react'
+import { useLocation, useNavigate, useRouter } from '@tanstack/react-router'
+import { isTelegramApp } from '@/hooks/useTelegram'
+
+export function useAppGoBack(): () => void {
+    const navigate = useNavigate()
+    const router = useRouter()
+    const pathname = useLocation({ select: (location) => location.pathname })
+
+    return useCallback(() => {
+        if (!isTelegramApp()) {
+            router.history.back()
+            return
+        }
+
+        if (pathname.startsWith('/sessions/')) {
+            navigate({ to: '/sessions' })
+            return
+        }
+
+        if (pathname.endsWith('/spawn')) {
+            navigate({ to: '/machines' })
+            return
+        }
+
+        if (pathname.startsWith('/machines')) {
+            navigate({ to: '/sessions' })
+        }
+    }, [navigate, pathname, router])
+}