Implement package testing in ASP.NET Core repo

### Is there an existing issue for this?

- [X] I have searched the existing issues

### Describe the bug

Adding health checks with AddHealthChecks().AddCheck() prevents calls to `IHealthCheckPublisher.PublishAsync`.

### Expected Behavior

I expect `IHealthCheckPublisher.PublishAsync` to be called where `.AddCheck` has been called or not.

### Steps To Reproduce

https://github.com/anvilcloud/HealthChecksRepro

### Exceptions (if any)

None.

### .NET Version

7.0.100

### Anything else?

**IDE**
Microsoft Visual Studio Professional 2022 (64-bit) - Current
Version 17.4.2

**dotnet --info**
```
.NET SDK:
Version: 7.0.100
Commit: e12b7af219

Runtime Environment:
OS Name: Windows
OS Version: 10.0.19044
OS Platform: Windows
RID: win10-x64
Base Path: C:\Program Files\dotnet\sdk\7.0.100\

Host:
Version: 7.0.0
Architecture: x64
Commit: d099f075e4

.NET SDKs installed:
7.0.100 [C:\Program Files\dotnet\sdk]

.NET runtimes installed:
Microsoft.AspNetCore.All 2.1.30 [C:\Program Files\dotnet\shared\Microsoft.AspNetCore.All]
Microsoft.AspNetCore.App 2.1.30 [C:\Program Files\dotnet\shared\Microsoft.AspNetCore.App]
Microsoft.AspNetCore.App 3.1.31 [C:\Program Files\dotnet\shared\Microsoft.AspNetCore.App]
Microsoft.AspNetCore.App 6.0.11 [C:\Program Files\dotnet\shared\Microsoft.AspNetCore.App]
Microsoft.AspNetCore.App 7.0.0 [C:\Program Files\dotnet\shared\Microsoft.AspNetCore.App]
Microsoft.NETCore.App 2.1.30 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.NETCore.App 3.1.31 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.NETCore.App 5.0.17 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.NETCore.App 6.0.9 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.NETCore.App 6.0.11 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.NETCore.App 7.0.0 [C:\Program Files\dotnet\shared\Microsoft.NETCore.App]
Microsoft.WindowsDesktop.App 3.1.31 [C:\Program Files\dotnet\shared\Microsoft.WindowsDesktop.App]
Microsoft.WindowsDesktop.App 6.0.11 [C:\Program Files\dotnet\shared\Microsoft.WindowsDesktop.App]
Microsoft.WindowsDesktop.App 7.0.0 [C:\Program Files\dotnet\shared\Microsoft.WindowsDesktop.App]

Other architectures found:
x86 [C:\Program Files (x86)\dotnet]
registered at [HKLM\SOFTWARE\dotnet\Setup\InstalledVersions\x86\InstallLocation]

Environment variables:
Not set

global.json file:
Not found

Learn more:
https://aka.ms/dotnet/info

Download .NET:
https://aka.ms/dotnet/download
```

**Update:** This works if the `TargetFramework` is set to `net7.0`. Unfortunately I need to do this in `net6.0`.