[WebToolsE2E][Aspire] When running dotnet watch for Aspire Starter App, the dashboard URL gets opened without the login token applied

**REGRESSION INFO**
Not a regression. Also reproduces with SDK 9.0.102 (included in VS 17.12.4)

**INSTALL STEPS**

1. Clean machine: Win11 x64 23h2 ENU
1. Install SDK 9.0.200-preview.0.25057.12 (was included as part of my install of VS 17.13 Preview 3 candidate build, Web workload)
1. Install Aspire 9 templates
- `dotnet new install Aspire.ProjectTemplates --force`

**REPRO STEPS**

1. Go to browser settings > delete localhost cookies

1. Create app using aspire-starter template and run using `dotnet watch`
- Open CMD, create an aspire starter app using following code
```
dotnet new aspire-starter -o Aspire9StarterApp02
cd Aspire9StarterApp02\Aspire9StarterApp02.AppHost
dotnet watch
```

**ACTUAL**

The browser opens the dashboard login URL automatically, but without the token applied. So, you need to manually enter the token value to log in.



**EXPECTED**
The token should be passed to the login URL so that the login happens automatically and we can view the dashboard