  The detection of the quantum nature of gravity in the low-energy limit hinges
on achieving an unprecedented degree of force sensitivity with mechanical
systems. Against this background, we explore the relationship between the
sensitivity of mechanical systems to external forces and the properties of the
quantum states they are prepared in. We establish that the main determinant of
the force sensitivity in pure quantum states is their spatial delocalisation
and we link the force sensitivity to the rate at which two mechanical systems
become entangled under a quantum force. We exemplify this at the hand of two
commonly considered configurations. One that involves gravitationally
interacting objects prepared in non-Gaussian states such as Schr\"odinger-cat
states, where the generation of entanglement is typically ascribed to the
accumulation of a dynamical phase between components in superposition. The
other prepares particles in Gaussian states that are strongly squeezed in
momentum and delocalised in position where entanglement generation is
attributed to accelerations. We offer a unified description of these two
arrangements using the phase-space representation and link their entangling
rate to their force sensitivity, showing that both configurations get entangled
at the same rate provided that they are equally delocalised in space. Our
description in phase space and the established relation between force
sensitivity and entanglement sheds light on the intricacies of why the
equivalence between these two configurations holds, something that is not
always evident in the literature, due to the distinct physical and analytical
methods employed to study each of them. Notably, we demonstrate that while the
conventional computation of entanglement via the dynamical phase remains
accurate for Schr\"odinger-cat states, it yields erroneous estimations for
systems in squeezed cat states.
