Can anyone suggest an audio program (preferably for Linux) that can help
isolate Biden's voice? Computery techniques I could use, or you could
use, to help figure out what he's whispering?

Do you have software development skills?

The best solution is likely to train or fine tune something like Mozilla DeepSpeech around obstructed human whispers.

To do that you'll need a way of generating similar whispers. This means simulating cover noise overlayed on the DeepSpeech training data.