Does recording desktop audio reduce quality? If I record audio (say, a 320 kbps mp3) that's playing through my desktop audio (in, for example, Audacity with loopback, or OBS) is the quality going to be reduced if I compare the recording to the original file? For the sake of this hypothetical lets assume the compression level of the rendered recording is also 320kbps mp3.

Does the act of recording the audio in this manner inherently reduce the quality? (regardless of compression method e.g. .wav to .wav)
Does reencoding/compressing the audio from 320kbps mp3 to 320kbps mp3 result in a measurable quality loss?
Audacity would grab the digital data for recording in this case and since it uses a lossless format for recording you would not lose any information. I don't know about OBS but it would be surprising if they do things differently.

There will be a very slight loss of quality with 320 kbps mp3s. I doubt any human would hear a difference, though. This may become noticable at some point if you keep re-encoding the file again and again, for example for editing the audio later. If you use a low quality source, say 128 kbps mp3, the degradation will be much more pronounced.