It may sound a bit weird for anyone not familiar with blockchain why it is not possible to withdraw to Brave wallet. But there is an explanation.
Brave wallet is a cryptocurrency wallet. All transactions are performed on-chain and de-fi.
Brave rewards are a virtual token that it is only valid while you watch ads in your browser. It is not a crypto token and it is not managed on-chain.
If you connect Uphold or Gemini to your rewards wallet, then, at the end of the month, those virtual tokens will be credited into your custodial wallet. Which, by the way, it is still off-chain. The balance only exists on their accounts.
In order to transfer to your Brave wallet, you must withdraw from your Uphold or Gemini account. This is the moment the transaction is performed on-chain.
So, technically, it is not possible to transfer a virtual token off-chain into a wallet that only works on-chain.
On top, due to regulations, it is not possible to withdraw without a KYC verification. Thus why Brave uses Uphold and Gemini.