Everything on teia.cafe (and teia.art) runs on a Tezos wallet instead of an account - no databases, no logins. There is no sign-up and no password that is stored anywhere - you bring a wallet, and that wallet is your identity everywhere on the site, and your identity everywhere in the world. (Your wallet and keys are unique only to you.)
Some suggestions to help you get started, including a widget to test the synchronization process.
Test your wallet
Press the button and pick your wallet. It only says hello - there is nothing to sign, nothing to approve, and it costs nothing. If your address appears, your wallet is set up correctly.
Kukai runs on a web page, so it is the shortest path from nothing to a working wallet. Good if you want to be up and running in a few minutes. wallet.kukai.app
Your recovery phrase is the wallet. Not a password, not a backup code - the words themselves are the money. Nobody can reissue them, and anyone who reads them owns everything in the wallet. Written on paper, offline, is still the best answer.
Nobody legitimate will ever ask for it. Not teia.cafe, not the Teia DAO, not a helpful stranger in a Discord. Every single person who asks is stealing from you, without exception.
Read what you are signing. Connecting a wallet is harmless - it shares an address and nothing more, which is all the check above does. Signing is the part that can move things. A wallet that asks you to sign when you only clicked connect is worth backing out of.