This requires the use of an Interactive Object with the web3-enabled website URL placed as input in the Embedded Website field. This allows you to open the website inside a Gather Space by approaching the object and pressing X.
Connecting the Wallet
Method 1: Walletconnect
Some web3 apps allow the use of Walletconnect.
This makes it easy to use in Gather. Choose the Walletconnect method of signing in, and scan the QR code with your Walletconnect-enabled phone wallet app.
Method 2: Metamask Wallet + Browser Cookies
Log in to the Metamask browser extension.
Approach the Interactive Object and press x.
The website should popup as an embed in the Gather Space.
Ta-da! It recognizes your wallet, and you can even sign transactions via Metamask!