[AspireE2E] When running a project with '.dev.localhost TLD' checked for the first time, you will need to enter a token.

**REGRESSION INFO**: Not a regression

**INSTALL STEPS**
1. Clean machine: Win11 x64 23h2 ENU
2. Install SDK 10.0.100
- Add .NET 10.0 feed
3. Install VS Code - 1.105.1
- Install latest public prerelease C#DK
4. Add feed for Aspire 13.0
5. dotnet new install Aspire.ProjectTemplates::13.0.0 --force

**REPRO STEPS**
1. Open VS Code > Create .NET Project > Aspire Starter App[net10.0, aspire 13.0] > Check 'Use the .dev.localhost TLD in the application URL' > Create
2. Right click the AppHost project > Debug > Start New Instance

**NOTE**:
1. This issue will not be reproduced if 'Use the .dev.localhost TLD in the application URL' is not checked.
2. This issue will not be reproduced when creating and running a project using CMD.
3. This issue only occurs the first time a project with 'Use the .dev.localhost TLD in the application URL' checked is run. If the token has been entered once, running an existing project or a new project will not reproduce this issue.

**ACTUAL**
The first time you run it, you need to enter a token to log in.

**EXPECTED**
No need to enter a token.

Start by reproducing the Aspire Starter App flow in VS Code with “Use the .dev.localhost TLD in the application URL” enabled, then use AppHost > Debug > Start New Instance. Compare the first-run VS Code behavior with the CMD flow and with a project after the token has already been entered. Done means the first run no longer prompts for a token.

Written by the indexing model from the issue text.