Thank you @ErikaC for your answer. I am connecting the sensor without any signal conditioning. For my test bench I measure V_out from the sensor directly with an oscilloscope with 80 MSPS. I use this as a DAQ system, as I am only interested in a relatively short time span, which in turn I need in a relatively high temporal resolution. For this, 1 ms is actually much too slow. Unfortunately, I have not found any differential pressure sensors with a higher time resolution.
How I can understand the response time is still not entirely clear to me. The time of 1 ms is always required, regardless of how high the change in differential pressure at the sensor input is? So whether the output voltage rises from 200mV to 209mV or to 300mV is irrelevant, the response time is always 1 ms?
That would mean that I always have a delay of 1 ms in my output signal in respect to the change in the input. And also that the sensor can only start to convert the differential pressure from the input into the output voltage again after 1 ms, i.e. a time resolution of 1 ms.
Can this be assumed?