I wonder if there's a way for computers to self-measure round trip. Even if you have to plug an aux cord between the speaker + mic jacks.

My first paper as an undergrad measured MIDI round-trip by tapping the input and output MIDI wires and then looking at how the signals were offset: https://www.kmjn.org/publications/MIDI_ICMC04-abstract.html

For keyboard input, one paper (whose citation I can't seem to find) used a clicky mechanical keyboard, pointed a mic at the computer, and measured the offset between each corresponding pair of keyboard click and sound output.

That is the way to do it. In Ardour it is part of the audio setup.

People have done experiments using high-speed cameras and such.