So, I just walked into an area, "Park Street Station," doing the quest "Unlikely Valentine."

Not in combat when this happens... Piper just sits down, as if maybe injured, even though she was just walking. Now, she won't sit up, she just refreshes her location every now and then, and I can't give her a stim to make her move, and she doesn't follow any commands other than taking them as input. Is there maybe a console command to reset her status until the bug is fixed?

Have you tried walking further away from her? She should get up and follow. If that doesn't work, try ~EvaluatePackage.