Pressure sensor assembly and corresponding device and insert

A pressure sensor assembly (1) for detecting the pressure of a fluid, comprising:-a pressure-sensitive member (2) having a substantially cup-shaped sensor body (5) comprising a bottom portion (5a) defining an axial cavity (C1, C2) and a peripheral portion (5b), the bottom portion (5a) comprising an elastically deformable membrane portion closing the axial cavity (C1, C2) at one end of the sensor body (5), and the peripheral portion (5b) has a distal edge opposite the bottom portion (5a) defining an inlet for the axial cavity (C1, C2), the bottom portion (5a) having at least one element associated therewith for detecting deformation of the membrane portion; and-a compensation element (3) configured for compensating for possible changes in the volume of the fluid, the compensation element (3) comprising at least one compensation body (8) made of a first elastically deformable or compressible material and a core (9) to which the at least one compensation body (8) is fixed, the core (9) being made of a second mat