--dotnet-isolated-debug does not emit process ID when logLevel.Host=Error

The --dotnet-isolated-debug argument does not emit process ID when logLevel.Host=Error.

Repro steps

• Create a new Azure Functions project, V4, with the .NET Isolated Worker.
• Add one function, for example an HTTP trigger
• Add the following host.json:

{
    "version": "2.0",
    "logging": {
        "applicationInsights": {
            "samplingSettings": {
                "isEnabled": true,
                "excludedTypes": "Request"
            }
        },
        "logLevel": {
            "default": "Warning",
            "Host": "Error",
            "Function": "Information"
        }
    }
}

• Run func.exe host start --pause-on-error --dotnet-isolated-debug on the terminal

Expected

The following output is written to console:

Azure Functions Core Tools
Core Tools Version:       4.0.4483 Commit hash: N/A  (64-bit)
Function Runtime Version: 4.1.3.17473

[2022-05-17T05:47:08.069Z] Azure Functions .NET Worker (PID: 19708) initialized in debug mode. Waiting for debugger to attach...

Actual

No worker process id is written to console, and attaching a third-party debugger automatically is not possible.

Extra information

Setting the environment variables FUNCTIONS_ENABLE_DEBUGGER_WAIT=True and FUNCTIONS_ENABLE_JSON_OUTPUT=True in addition does also not emit the PID.