2001 Prius with steering wheel and key locking?

Our 2001 Prius has recently been having problems with the steering wheel locking (not in a position where this would be normal/expected, but in random positions--takes several minutes of wiggling and turning the car on and off to get it unlocked) and the key getting stuck in the ignition (just as if the car weren't in park, except that it is). They might be unrelated, but started occurring at the same time.

Anyone else experience this and have any idea what could cause it? In forums for the Gen II and beyond it seems the key problem could be a dying 12V battery, but not clear if that would also be the case for the Gen I with no power button. I'd love any ideas anyone has--thanks! It's happening intermittently enough that I haven't called our repair shop yet, but will if it continues or if there's a clear culprit.

 

Not sure this helps for your situation if it improved, but I think I've figured out ours--shortly after posting this we developed a third problem where the key would not properly turn the door cylinder--felt like molasses and then triggered horn beeping as if the car thought it was being broken into. Super strange. But I think that likely means we have a failing key (not super surprising after so many years, I guess!) Not sure exactly why that would cause the other two issues but they are also both things that involve the key (in the ignition cylinder) so that may be the link. Switching to our spare key and will see if the problems go away!