I bought a used Steinway. Sometimes its keys don't always make a sound when pressed down. Is this my fault or the piano's?
Should I contact the seller, or is it a minor problem that the tuner can fix in a few weeks when it's settled?
Ask the piano tuner to regulate the action, especially if the piano's move underwent changes of humidity. Some keys' pivots may have become sticky. In the meantime, if one key often suffers from a silent depress, bang away at it fast and loud for a minute. That could loosen it up, and certainly won't hurt it.
If you just bought a Steinway, it's a reasonable assumption that you already can play the piano, so it's unlikely to be "your fault" that you can't play a note.
It could just be a temporary thing caused by change of humidity or temperature. I once had an upright piano where this happened to almost every key a few days after it was moved, but week later it was back to normal without any adjustments when all the working parts had acclimatized to the new environment.
Whatever the cause, you need to get a professional to look at it if the cause of the problem is not obvious to you.
We don't know anything about the instrument, but just because it's a Steinway doesn't mean it is guaranteed to be in good condition if it has never been looked after. Let's hope you haven't made the mistake of buying a Steinway nameplate attached to an overpriced heap of firewood and scrap metal!
The fact that you said "the seller" and not "the piano dealer" or "music shop" might mean you bought it from a private individual, so I hope you got a professional valuation on the instrument if you paid a lot of money for it. If it seemed like a bargain because of the maker's name plus a low price tag, you might have just found out why the seller wanted to get rid of it.
(Sorry, but I'm a pessimist by nature!)