What about using a pressure sensor fixed to a long pole in front of the submarine? That way, if they hit anything, the pole would hit first, and could activate the stopping mechanism.

These things can't stop on a dime.

How long would the pole have to be to stop a 40mph submarine?

You could probably find the data you need here:

https://core.ac.uk/download/pdf/36725639.pdf

Imagine swimming with a long pole attached to the front of you. Even if it would be thin, it would still disturb you very much. Also the disturbances in the water created by the pole would make noise, that can be detected.

Submarines are optimised in everything for absolute stealth, up to the point that the crew may not make any noise, like dropping a wrench.

Wouldn't a small drone make less noise than a submarine?

That seems intuitive but one thing I've learned in my career is that obvious easy ideas that nobody does are usually missing key details.

A small drone and a submarine would make more noise than either alone.

Noise from the drone propeller?