Namebase is
a registry now.
You followed a link to the dashboard on the old Namebase. That service was custodial: it held the keys, the coins and the names on your behalf. It has been retired, and nothing here holds a key for anybody any more.
Still holding HNS or names?
They are still yours and still withdrawable. Create a wallet first so you have an address of your own, then use the withdrawal tool to send your HNS and transfer your names to it. There is no old recovery phrase to import, because the previous service held those keys for you.
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.