[AspireE2E] When running the project from the output path using Aspire run, it keeps displaying "Connecting to apphost..."

**REGRESSION INFO**: Not repro on Aspire CLI version 13.1.3

**INSTALL STEPS**

1. Clean machine: Windows x64 25h2
2. Install SDK 10.0 201
3. Install Aspire.CLI 13.2.0
- iex "& { $(irm https://aspire.dev/install.ps1) } -Quality staging"
- aspire config set -g features:stagingChannelEnabled true

**REPRO STEPS**
1. Open a normal Command Prompt
2. Use `aspire new` to create a Starter App (ASP.NET Core/Blazor) project.
3. Go to the output path folder (Not the AppHost project folder) and run the app with `aspire run`

**NOTE**: If navigate to the AppHost project folder and run the app with `aspire run`, it will run successfully.

**Actual Result**
It keeps displaying "Connecting to apphost..."

**Expected Result**
It can run successfully.

Reproduce the issue on Windows with Aspire CLI 13.2.0 by running `aspire run` from the generated output path, then compare it with running from the AppHost project folder. Start by tracing the CLI's project discovery and apphost connection handling; done means the output-path command connects and runs successfully.

Written by the indexing model from the issue text.