Namebase is
a registry now.
You followed a link to .gdcoin on the old Namebase. That service was custodial: it held the keys, and the names, on your behalf. It has been retired, and nothing here holds a key for anybody any more.
Handshake auctions still run, on chain, every day. Bidding in one now means holding your own keys and running your own node, which is what the wallet is for. Your names stay yours whether or not this site exists.