You can pick a lock to the room which the key is for that you need to find in order to actually complete the mission. I picked the lock as I did not see the key initially and was wondering why the mission would not complete.
I suggest to rephrase the step with the key to “Find a way to get into that room”. Then you have two alternative ways and both should count.
Or you have to find the key, but then this second door should not be pickable.