fix(agent): align consumers with inbox lifecycle

apps/web/tests/smoke-real.e2e.ts

@@ -196,16 +196,19 @@ describe('dsh web keyless CLI smoke', () => {
       messages?: { role?: string; content?: string }[]
       tools?: { function?: { name?: string } }[]
     }
-    let resolveProviderRequest!: (request: NativeProviderRequest) => void
-    const providerRequest = new Promise<NativeProviderRequest>((resolve) => {
-      resolveProviderRequest = resolve
+    let resolveProviderRequests!: (requests: NativeProviderRequest[]) => void
+    const requests: NativeProviderRequest[] = []
+    const providerRequests = new Promise<NativeProviderRequest[]>((resolve) => {
+      resolveProviderRequests = resolve
     })
     const provider = createServer((request, response) => {
       let body = ''
       request.setEncoding('utf8')
       request.on('data', (chunk: string) => { body += chunk })
       request.on('end', () => {
-        resolveProviderRequest(JSON.parse(body) as NativeProviderRequest)
+        const parsed = JSON.parse(body) as NativeProviderRequest
+        if ((parsed.tools?.length ?? 0) > 0) requests.push(parsed)
+        if (requests.length === 2) resolveProviderRequests(requests)
         response.writeHead(200, { 'content-type': 'text/event-stream' })
         response.end([
           'data: {"choices":[{"delta":{"role":"assistant","content":null,"reasoning_content":""}}]}',
@@ -244,14 +247,21 @@ describe('dsh web keyless CLI smoke', () => {
         mode: 'queue',
         content: [{ type: 'text', text: 'go' }],
       })
-      const captured = await Promise.race([
-        providerRequest,
+      const capturedRequests = await Promise.race([
+        providerRequests,
         new Promise<never>((_resolve, reject) => {
           setTimeout(() => { reject(new Error('provider request not received in 10s')) }, 10_000).unref()
         }),
       ])
-      expect(captured.messages?.some(message =>
+      const initial = capturedRequests[0]
+      const captured = capturedRequests[1]
+      if (initial === undefined || captured === undefined) {
+        throw new Error('provider did not receive both workspace projection requests')
+      }
+      expect(initial.messages?.some(message =>
         message.role === 'user' && message.content?.includes('<available_skills>'))).toBe(false)
+      expect(initial.messages?.some(message =>
+        message.role === 'user' && message.content?.includes('web-workspace-context-probe'))).toBe(false)
       const workspaceMessage = captured.messages?.find(message =>
         message.role === 'user' && message.content?.includes('web-workspace-context-probe'))
       const systemMessage = captured.messages?.find(message => message.role === 'system')