How to detect whether door lock bolt/latch is pushed deep enough into hole/plate

I have several doors with a typical Abloy door lock mechanism. It works like a normal non-lock hatch, and locking works by the latch going deeper into the opposite plate - effectively turning it into a deadbolt. Now I would like to detect whether it is in “lock” position; in the further/deeper position. Both the bolt and plate are stainless steel. There’s not much space inside the hole where the bolt goes. There’s also maybe some 4mm change over the course of a year so it can’t be too precise.

What kind of sensor would be the best for detecting how deep the bolt is in the plate?

Here’s a video of the lock