Right. Then you wiped your computer. I’m assuming you did a fresh installation of Brave? If so, you created a new Rewards profile in doing so which would make you seem like a new user. The only possible way you would have kept anything is if you had done a backup of your \brave-browser or User Data folder and transferred that over. Even then, I’m not 100% sure if integration would have remained, but it used to at least.
But like it is said at PSA: Known issue with Gemini (Gemini is down), new profiles can’t connect.
Then there’s also all the conversation toward the bottom, such as PSA: Known issue with Gemini (Gemini is down) - #19 by chriscat and the following replies, you’d know that currently even existing accounts are having issues reconnecting.
Nope. Big thing is like you said, needs to be a custodial account and it must be with someone who has a contract with Brave. Brave Wallet is self custody and Brave has stated for many years it can’t pay out Rewards to it. I also have a thing written about why that and other things are necessary for Rewards in my FAQ, which you can see at PSA: Current FAQ