[WebToolsE2E][Green]Run the project in vs code for the first time, ".NET Hot Reload" in output window doesn't show up

[Susie-1989]

REGRESSION INFO: Repro in Nov release C# DK 1.90.2(C#2.110.4)

INSTALL STEPS

1. OS: window x64
2. Install the SDK 10.0.102
3. Install VS Code insiders - 1.109.0
4. Install Jan prerelease 2 prerelease C# DK1.92.5(include C#2.112.45)

REPRO STEPS

1. Go to Settings > Search 'Hot Reload' >Check "Enables C# Hot Reload while debugging“
2. Open vs code > Create .NET Project > ASP.NET Core Web App (Razor Pages)
3. Right click project > Debug >Start New Instance

Note:

1. If stop debugging, ".NET Hot Reload" show up, then re-run the project, ".NET Hot Reload" still show up
2. If uncheck "Enables C# Hot Reload while debugging“, launch vscode, run the project for the first time, ".NET Hot Reload" shows up, this behaviours is the same as vs

ACTUAL ".NET Hot Reload" doesn't show up

EXPECTED Should like VS, ".NET Hot Reload" show up

[Susie-1989]

Verify this issue in Feb prerelease 1 C# DK2.11.4(include C#2.121.32), the hot reload output window does not appear when running a project for the first time, it only appears after clicking the hot reload button