That wouldnt work.
When the object is touching the wall, the distance is zero. if the pressure is applied, the distance doesnt change anymore.
That would require moving the object into the wall to “apply pressure”.
You could however give the wall two states: A: Idle and B: Pushing.
In the idle state the wall does nothing. Its the default state.
When the object touches the wall it starts moving the wall along with itself (as if zerof pressure is needed to move it).
The object also switches the wall into pushing mode.
The pushing mode does the following:
On tick it saves its current position and the position of the pushing object. Then it compares its position with the previos position. If that delta change is below a certain threshold, move both, the object and wall back to its previous position.
When the object untouches, the wall should stop ticking, a.k.a. Idle mode.
This way you have to push “fast”, which is equivalent of using force/pressure.
If you want to do something like a snap feature, then just store the mouse position on contact and build the delta from there.