[AspireE2E] When I run the aspire project again with .WithReplicas(2) added using dotnet watch, the project fails to run successfully.

**INSTALL STEPS**

1. Clean machine: Win11 x64 23h2 ENU
2. Install SDK 10.0.101
3. Install Aspire.ProjectTemplates 13.1.0

**REPRO STEPS**

1. Open CMD and create aspire-starter project
```
dotnet new aspire-starter -o aspire01
cd aspire01/aspire01.AppHost
```
2. Add `.WithReplicas(2)` to AppHost.cs file of project and save
3. Dotnet watch the project in CMD, and open URL in the browser.
`dotnet watch`
4. Restarting one of the resources in the dashboard, the state of another resource becomes waiting. Then click the start button of another resource, it shows that the start is successful, but the state is Starting. Similar [issue](https://github.com/dotnet/aspire/issues/10650).
5. Stop running the project, and then run the project again using `dotnet watch`.

**ACTUAL**
The project status is not Running.

https://github.com/user-attachments/assets/147b0e4d-9ff8-4fca-b64c-c74c7a45f237

**EXPECTED**
All projects are running.