SIANXSVC-1206: dotnet-e5e writes logging messages after output in non-keepalive mode

[nachtjasmin]

Closes SIANXSVC-1206

To test it

1. Open the NativeAOT example (cd examples/NativeAOT)

2. Create a payload.json with the following contents:

   {"context":{"type":"integration-test","async":true,"date":"2024-01-01T00:00:00Z"},"event":{"type":"object","data":{"firstName":"Alexander","lastName":"Windbichler"}}}

3. Execute the example with the following command:

   dotnet run Hello ++ 0 ++ < payload.json
   

You should see both the logs and the output. In order to check that the redirection works as expected, redirect the stderr to /dev/null, like so:

dotnet run Hello ++ 0 ++ < payload.json 2> /dev/null

The only result is the JSON, with a leading ++. This matches the behaviour of go-e5e.

[PatrickTaibel]

Non-keepalive mode now works as intended (tested with our internal test function).