[AspireE2E] The start time displayed in the ACA dashboard does not refresh or update correctly when using the Start button to restart a stopped project.

**INSTALL STEPS**
1. Clean machine: Win11 x64 24h2 ENU
2. Install SDK 9.0.300
3. Add dotnet9 feed for 9.4.0
4. Install the latest Aspire 9.4.0
`- dotnet new install Aspire.ProjectTemplates::9.4.0-preview.1.25276.3 --force`
5. Install git and azd

**NOTES**
1. The ACA dashboard is version 9.2.1, but checking this issue with the Aspire 9.2.1 dashboard does not reproduce the issue.
2. This issue does not occur when restarting the project.

**REPRO STEPS**
1. Open CMD > Create aspire-starter app:
`dotnet new aspire-starter -o aspire1`
2. Publish the project
`cd aspire1/aspire.1apphost`
`azd init`
`azd up`
3. Click the link displayed in CMD to open the ACA dashboard.
4. Stop and start the project, then check the start time.

**ACTUAL**
The displayed start time does not refresh or update correctly.

https://github.com/user-attachments/assets/0b520647-b727-41b0-b7cd-66c63fae46c4

**EXPECTED**
After starting a previously stopped project using the Start button in the ACA dashboard, the start time should update to accurately reflect the new start time.