Came back to find a stranger's lock also securing my bike — what is the right move?

Both readings exist and it is worth knowing the bad one before you act.

The innocent version is common: someone puts a lock through what they think is their own frame in a crowded rack and catches yours. Happens constantly with two bikes leaning together.

The deliberate version is a known tactic. Immobilise a bike, wait for the owner to return, and see what happens. Some owners cut their own lock and leave in a hurry without re-securing properly; some abandon the bike overnight, which tells the person exactly where an unattended bike will be sitting at 3am. The conversation about your lock beforehand is the detail that makes me lean this way in your case, because it means someone examined your security before it happened.

Either way, the practical steps are the same, and the order matters.

The order I would use:

1. Photograph everything before touching anything. Both bikes, both locks, the railing, the surroundings, timestamps. This is your evidence if any of it becomes a dispute.
2. Leave a note with a phone number on the other bike, and wait a while if you can. A large fraction of these resolve in twenty minutes with an embarrassed apology.
3. Report it to the police or, if you are on private land, to the building or business. A report before you cut anything is what separates you from someone stealing a bike.
4. Get the other bike's details recorded — frame number if visible, description — and check whether it has been reported stolen. If it has, this becomes a very different conversation and not one for you to resolve.
5. Only then consider cutting, and cut your own lock rather than theirs. Yours is your property and destroying it raises no questions at all.

That last point is the one people get wrong. Cutting someone else's lock, even to free your own bike, puts you in a bad position.

If you do end up cutting your own lock, the thing that follows is that your bike is now unsecured in a place where somebody has taken an interest in it.

So have the replacement ready before you cut. Either bring a second lock with you, or arrange to move the bike straight into somewhere secure. Cutting free and then riding home is fine; cutting free and re-locking it in the same spot with nothing but a cable is how the second version of this story ends.

And if the deliberate reading is right, do not use that spot again for a while.

Worth adding a preventative that costs nothing: lock through the frame and the rail in a way that leaves no room for a second lock to pass through your frame.

A tight lock with little slack, positioned high on the frame triangle, is awkward for anyone to accidentally include. Most of the innocent cases happen because there was an obvious gap that looked like part of their own bike.