Is the pulse repeating or only occurs once on startup? If it repeats could be a PWM representation of T and RH.
What is connected on pin 1 and 4 in their system, any capacitors, resistors, etc.?
It doesn't look like PWM or SDM, there is no smooth signal of some duty cycle, there is a stream of random bits.
The circuit is unknown on the receiving side, both outputs are 10nF capacitors near the sensor.
To me it wouldn't make sense to have a 10nF capacitor on a data line. That is the recommended circuit for SHT30-ARP analog output version.
Maybe the analog output circuitry has been damaged.
"The first two digits XY (=AR) describe the output mode. The third letter (A) represents the manufacturing year (4 = 2014, 5 = 2015, etc). The last three digits (BCD) represent an
alphanumeric tracking code. That code can be decoded by Sensirion only and allows for tracking on batch level through production, calibration and testing – and will be provided upon justified request."
The part number you gave is for SHT30-ARP.