Ben Krasnow has uncovered a simple method for laser measurement. It will take some effort to convert it to a convenient tool, but he gave enough instructions to do that. Here is his video:
https://www.youtube.com/watch?v=MUdro-6u2Zg - "Laser diode self-mixing: Range-finding and sub-micron vibration measurement."
He found some laser diodes that have an integrated "internal monitor photodiode" with feedback. The feedback signal is what he is tracking. You get "interference" because the reflected wave timing matches the timing of the outgoing wave. So you should be able to get the same effect with an on purpose emitter and receiver pair.
I checked just now, and I think this "Self-mixing laser diode vibrometer December 2002" at https://www.researchgate.net/publication/228874101_Self-mixing_laser_diode_vibrometer is the same approach.
Looking more deeply, this paper 2004 "Self-Mixing Laser Diode Velocimetry: Application to Vibration and Velocity Measurement" by Lorenzo Scalise, Yanguang Yu, Guido Giuliani at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.474.4663&rep=rep1&type=pdf explains "
"Laser Doppler velocimetry and laser Doppler vibrometry are well-known measurement techniques widely used for the precise remote measurement of the velocity of fluids, and for accurate measurement of the displacement, velocity and acceleration of solid objects. With these types of instruments, it is possible to measure the velocity and displacement of the target surface, simply by using a light beam."
So there is a rich source of useful techniques - once you know to google "velocimetry" "laser" and "internal monitor photodiode".
Still further checking find "Microcantilever Displacement Measurement Using a Mechanically Modulated Optical Feedback Interferometer" at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4970047/ By 2016 they have broadened the concept from piezo to cantilever, and cleared up that it is an optical feedback loop.
Finally, "Optical feedback interferometry" today has over 10,000 results for the exact phrase.
Now to find one to adapt to my problem and move on. I just need a data stream.