[docs] Update Foundry hosted agent API from PublishAsHostedAgent to AsHostedAgent

src/frontend/src/content/docs/integrations/cloud/azure/azure-ai-foundry/azure-ai-foundry-host.mdx

@@ -347,11 +347,11 @@ await foundry
 </TabItem>
 </Tabs>
 
-`AddProject` creates a default Azure Container Registry for hosted agents. Use `WithContainerRegistry` when you want to point the project at a different registry.
+`AddProject` creates a default Azure Container Registry for hosted agents only in publish mode (when deploying to Azure). In local run mode, no default registry is created. Use `WithContainerRegistry` when you want to point the project at a specific registry.
 
-## Publish a hosted agent to Azure AI Foundry
+## Add a hosted agent to Azure AI Foundry
 
-Use `PublishAsHostedAgent` to publish an executable or containerized app as a hosted agent in a Foundry project:
+Use `AsHostedAgent` to configure an executable or containerized app as a hosted agent in a Foundry project:
 
 <Tabs syncKey='aspire-lang'>
 <TabItem id='csharp' label='C#'>
@@ -366,13 +366,13 @@ var chat = project.AddModelDeployment("chat", FoundryModel.OpenAI.Gpt5Mini);
 builder.AddPythonApp("agent-python", "..\\agent", "main:app")
     .WithReference(project)
     .WithReference(chat)
-    .PublishAsHostedAgent(project);
+    .AsHostedAgent(project);
 
 builder.AddProject<Projects.Agent>("agent-dotnet")
     .WithHttpEndpoint(targetPort: 9000)
     .WithReference(project)
     .WithReference(chat)
-    .PublishAsHostedAgent(project);
+    .AsHostedAgent(project);
 
 builder.Build().Run();
 ```
@@ -397,22 +397,22 @@ await builder
   .addPythonApp('agent-python', '../agent', 'main:app')
   .withReference(project)
   .withReference(chat)
-  .publishAsHostedAgent({ project });
+  .asHostedAgent({ project });
 
 await builder
   .addProject('agent-dotnet', '../Agent/Agent.csproj')
   .withHttpEndpoint({ targetPort: 9000 })
   .withReference(project)
   .withReference(chat)
-  .publishAsHostedAgent({ project });
+  .asHostedAgent({ project });
 
 await builder.build().run();
 ```
 
 </TabItem>
 </Tabs>
 
-In run mode, `PublishAsHostedAgent(...)` configures a local `http` endpoint for the agent. Aspire first checks whether the resource already has an endpoint named `http`. If that endpoint has a target port, Aspire preserves it. If there is no existing `http` target port, Aspire defaults to `8088`.
+In run mode, `AsHostedAgent(...)` configures a local `http` endpoint for the agent. Aspire first checks whether the resource already has an endpoint named `http`. If that endpoint has a target port, Aspire preserves it. If there is no existing `http` target port, Aspire defaults to `8088`.
 
 Aspire also injects the selected port as `DEFAULT_AD_PORT`, so hosted-agent apps can bind to the right port:
 
@@ -421,7 +421,7 @@ var port = Environment.GetEnvironmentVariable("DEFAULT_AD_PORT") ?? "8088";
 builder.WebHost.UseUrls($"http://+:{port}");
 ```
 
-If your hosted agent listens on a different port, declare the endpoint before calling `PublishAsHostedAgent(...)`:
+If your hosted agent listens on a different port, declare the endpoint before calling `AsHostedAgent(...)`:
 
 <Tabs syncKey="aspire-lang">
 <TabItem id="csharp" label="C#">
@@ -432,7 +432,7 @@ var dotnetWeatherAgent = builder.AddProject<Projects.WeatherAgent_Dotnet>("weath
     .WithReference(project).WaitFor(project)
     .WithReference(chat).WaitFor(chat);
 
-dotnetWeatherAgent.PublishAsHostedAgent(project);
+dotnetWeatherAgent.AsHostedAgent(project);
 ```
 
 </TabItem>
@@ -450,7 +450,7 @@ const dotnetWeatherAgent = await builder
   .withReference(chat)
   .waitFor(chat);
 
-await dotnetWeatherAgent.publishAsHostedAgent({ project });
+await dotnetWeatherAgent.asHostedAgent({ project });
 ```
 
 </TabItem>
@@ -537,7 +537,7 @@ Prompt agents are deployed to Azure AI Foundry even during local development. Lo
 
 ## Invoke agents from the Aspire dashboard
 
-Aspire also makes the declared agents easy to try from the dashboard. Prompt agents get a **Send Message** command from `AddPromptAgent(...)`. Hosted agents published with `PublishAsHostedAgent(...)` get a highlighted **Send Message** command that posts to the local `/responses` endpoint, plus dashboard links for `/responses`, `/liveness`, and `/readiness`.
+Aspire also makes the declared agents easy to try from the dashboard. Prompt agents get a **Send Message** command from `AddPromptAgent(...)`. Hosted agents configured with `AsHostedAgent(...)` get a highlighted **Send Message** command that posts to the local `/responses` endpoint, plus dashboard links for `/responses`, `/liveness`, and `/readiness`.
 
 <ThemeAwareImage
   dark={agentSendMessage}