To answer the last part of that question which is "does the fish bioacoustics community use pressure-gradient hydrophones"-
Yes, often the two hydrophone method is used to estimate particle motion, but that is only appropriate where propagation conditions are suitable for the method. The two hydrophone method requires high quality hydrophones that can make accurate phase measurements, and then a fair bit of expertise to work out what's going on.
There are a few commercially available sensors which directly measure water-borne particle motion (velocity or acceleration). A few research groups have access to these sensors, but not many, and they are definitely not a common piece of kit. An example of such a sensor is: https://geospectrum.ca/commercial-products/directional-sensors/particle-motion/
It has taken a long time for the underwater bioacoustics community to learn/accept that some fish and invertebrates are sensitive to particle motion alone (rather than pressure), which sort of explains the lag in available sensors. Plus, it's sort of tricky to make a particle velocity sensor for water that is accurate.
For more info on the water-borne side, see:
Popper, A. N., and Hawkins, A. D. (2018). “The importance of particle motion to fishes and invertebrates,” J. Acoust. Soc. Am., 143, 470–488. doi:10.1121/1.5021594