refactor(mobile-web): put the transport connection state on the wire

The shell collapsed six transport states into four, and every page route
expanded them back. Both mappings are gone; the page reads the state the
transport reported.

Claude-Session: https://claude.ai/code/session_01JNnE9qzUZMMnqpZWCqM3nb

src/mobile-web/src/native-shell-channel.ts

@@ -15,6 +15,7 @@ import {
   parseMobileWebBridgeInitialMessage,
   parseMobileWebBridgeShellMessage,
   type MobileWebBridgeMessageContext,
+  type MobileWebConnectionState,
   type MobileWebNavigationRoute,
   type MobileWebResumeRoute
 } from '../../shared/mobile-web/bridge-contract'
@@ -29,7 +30,7 @@ import { subscribeToMobileWebShellMessages } from './native-shell-message-inbox'
 export type MobileWebNativeShellState = {
   client: MobileWebBridgeClient | null
   context: MobileWebBridgeMessageContext | null
-  connection: 'connecting' | 'connected' | 'offline' | 'recovering'
+  connection: MobileWebConnectionState
   hostDisplayName: string | null
   reconnectAttempts: number
   lastConnectedAt: number | null

src/shared/mobile-web/bridge-contract.test.ts

@@ -516,7 +516,7 @@ describe('mobile web bridge shell contract', () => {
       type: 'connection',
       shellSessionId: SHELL_SESSION_ID,
       buildId: BUILD_ID,
-      state: 'recovering'
+      state: 'reconnecting'
     }
 
     expect(

src/shared/mobile-web/bridge-contract.ts

@@ -165,7 +165,16 @@ const ShellEnvelopeSchema = z.object({
   buildId: BuildIdSchema
 })
 
-const ConnectionStateSchema = z.enum(['connecting', 'connected', 'offline', 'recovering'])
+// The shell publishes the transport's own state; the page decides what to show for each.
+const ConnectionStateSchema = z.enum([
+  'connecting',
+  'handshaking',
+  'connected',
+  'disconnected',
+  'reconnecting',
+  'auth-failed'
+])
+export type MobileWebConnectionState = z.infer<typeof ConnectionStateSchema>
 const ConnectionMetricsShape = {
   reconnectAttempts: z.number().int().nonnegative().max(1_000_000).optional(),
   lastConnectedAt: z.number().int().nonnegative().max(Number.MAX_SAFE_INTEGER).nullable().optional()