New Shepard had two separate sensors for ground proximity, for its flights on 2020 Oct 13 and 2021 Aug 16.
Section III of New Shepard Flight Test Results from Blue Origin De-Orbit Descent and Landing Tipping Point, by Bieniawski et al, AIAA 2022-1829, reports:
The final set of sensors included the NDL [Navigation Doppler
LiDAR] from NASA Langley, the DLC [Descent and Landing Computer]
from NASA JSC, and the OMPS [Optical Moon Proximity Sensor]
procured from OADS [Optical Air Data Systems]. The NDL consists of an
electronics box and laser connected by fiber optic cables to three
telescopes mounted at fixed angles within one of the transition
tunnels.
The NDL sends near infrared (1550 nm wavelength) laser
beams to the surface, and the reflected returns are detected to
provide an estimate of the lander’s velocity and range relative to the
ground.
...
The OMPS ... consists
of a small electronics box and four telescopes. The measurement
principle, while still a LiDAR at 1550 nm wavelength, is different
from the NDL and leverages OADS’s years of development in terrestrial
LiDARs for wind turbines, helicopters, and aircraft.
The NDL LiDAR is documented here.
The NDL was the one used for real-time navigation, while the OMPS's measurements were only recorded for post-flight evaluation.
Correction: The NDL and OMPS were mounted near the top of the booster, rather than on the crew capsule, as shown in part of figure 4 in the paper (below), and as implied by figure 12 which is a photo of the booster just before landing annotated with laser directions.

Blue Origin's fact sheet says that
Right before touching down, a retro thrust system expels a cloud of air beneath the capsule to create a gentle landing around 1 mph in the West Texas desert.
This retropropulsion (not a rocket, just a tank of compressed air?) must be commanded by software just like all aspects of its flight. But I don't know what kind of sensor triggers that command.