I bought a starter from a bakery, and I think I overfed it overnight. It overflowed from its jar. What should I do now?
All you need to do is clear up the mess, and make use of the active starter. Maybe find a bigger jar as well.
You've got a good healthy starter by the sounds of things. If it's from a bakery it's probably used to being used daily; home bakers often keep starters in the fridge. For example I take mine out a few hours before feeding, assemble my loaf another few hours later, then put it back in the fridge. It will evolve for your kitchen anyway, but if you do go for fridge storage, it will have to adapt a bit more.
Cleaning it up isn't all that easy. It ideally needs to be really wet but really dry means it can chip off surfaces.
What you do should now? You should be happy to have a good and active starter, clean up the mess and proceed feeding what’s left in the jar - with a larger jar or less starter.
Seriously, apart from the mess, there’s nothing wrong. I guess it’s happened to most of us, me certainly. A well-fed, active sourdough will easily double in volume and depending on its characteristics (they can behave differently, due to the particular composition of yeasts and bacteria) and environmental factors, I have seen some almost tripling.
So I never fill my jars more than 1/3, maybe 2/5 if I have a particularly sluggish one on a cold day. A lid can help prevent overflowing to some degree, but it shouldn’t be tight-fitting and it will not work if there’s a lot of expansion.