[BUG] Log output from Azure Functions host not redirected to Aspire dashboard

[captainsafia]

Describe the Issue

When launching an Azure Functions project in an Aspire host with the new support, log outputs from the Functions host are only emitted to the task output in VS Code and not to the Aspire dashboard.

Steps To Reproduce

1. Clone https://github.com/captainsafia/PigLatinApp.
2. Open PigLatinApp.AppHost/Program.cs and F5 to start debugging the associated project.
3. Observe that logs for the Functions host are only emitted to the task output in VS Code and not the log pane in Aspire.

Expected Behavior

Logs should be visible in both the Aspire dashboard and the VS Code task output window.

Environment Information

OS: macOS 15.1
VS Code Version: 1.95.2, Commit: e8653663e8840adaf45af01eab5c627a5af81807

Name: C# Dev Kit
Id: ms-dotnettools.csdevkit
Description: Official C# extension from Microsoft
Version: 1.13.6 (prerelease)

Name: C#
Id: ms-dotnettools.csharp
Description: Base language support for C#
Version: 2.55.21 (pre-release)

[captainsafia]

cc: @WardenGnaw

[mattchenderson]

We believe microsoft/vscode-azurefunctions#4745 would provide the right solution to this. I propose using this item to track C# Dev Kit absorbing any changes there and adding in the appropriate redirects.