I won an auction — how do I get the NFT?

Claim it. After the auction ends, open it, from Profile → Won or your notification, and press Claim this NFT. Your bid has already paid for the item. Claiming moves it from the auction into your wallet, for a small POL fee.

Until you claim it, the item is yours but is not in your wallet, so it does not appear under NFTs. The claim does not expire. Claiming needs the wallet that placed the winning bid, but you do not need to be signed in.