dcp `Starting Process` message shows up after application output has been written

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Describe the bug

For processes, aspire recently started logging `[sys] Starting process...: Cmd = C:\Program Files\nodejs\npm.cmd, Args = ["run", "dev", "--", "--port", "59291"]` to the console logs

However I've found that if often gets interleaved with the actual command output in weird ways - often appearing in the middle of logs from after the application has started.

### Expected Behavior

I'd expect the `[sys] Starting process...: Cmd = C:\Program Files\nodejs\npm.cmd, Args = ["run", "dev", "--", "--port", "59291"]` log to come before any output from the process.

### Steps To Reproduce

_No response_

### Exceptions (if any)

_No response_

### .NET Version info

_No response_

### Anything else?

_No response_