Why would a new water heater's PRV leak when the PRV on the old heater never leaked?
PRVs are designed to release pressure.   Heating water increases the size of the water and the pressure.  Your new water heater is likely heating the water quicker due to newer elements, less sediment in the bottom or other factors.  Heating the water quicker will cause the pressure to increase over a smaller amount of time which might trigger the PRV.  Do you have an expansion tank?
Your old PRV might have been defective or less sensitive or the new PRV could be more sensitive.  Do you have a pressure gauge can you tell what pressure it is releasing at?  There are pressure gauges that you can screw onto hose bibs so you can attach them to the tank drain and monitor.
Homedepot has some for $10.  Water Pressure Test Gauge.
https://www.homedepot.com/p/Watts-3-4-in-Plastic-Water-Pressure-Test-Gauge-DP-IWTG/100175467