Brave Wallet is simply a place where you can send and receive crypto that’s on chain. Rewards payments currently are not able to be sent directly to Brave Wallet because they are not serving as money exchangers and also will not be doing KYC/AML.
In order for you to get the exchange of virtual Basic Attention Token (vBAT) and convert it to Basic Attention Token (BAT), it needs to go through the custodial partners.
You may want to try to read through things at PSA: Current FAQ
For example: