Problem:
The Brave browser with MetaMask extension is not connecting to 1inch.io. First icon in the 'connect wallet' section is displayed as 'Web3' instead of 'MetaMask'.
Solution:
open your Brave menu by clicking ≡ in the upper right corner;
'settings' → 'extensions' (brave://settings/extensions);
change 'Web3 provider for using Dapps', set 'MetaMask' there;
restart the Brave browser;
go to https://app.1inch.io/, click "connect wallet" and select first option 'MetaMask'.