Well, it’s like I said in the one you’re replying to…
So yeah…if you’ve been connected then you are just logged out on the browser side but you’ll continue receiving payments as they have you connected on the back end.
As to reconnecting, it’s been a very long time of people experiencing this issue.
You can essentially look through Gemini Logged Out and "Your Request Is Still Being Processed" Issue FAQ
But then you might also want to check out links I listed at PSA: Known issue with Gemini (Gemini is down) in regards to issues Gemini has been having.
Your best bet is probably to leave things alone for the moment. On chain payments should be coming before long. They just did one of the first official teasers on it today with https://brave.com/boomerang/ announcement. Once they move on to this, then you’ll be able to just receive your BAT directly rather than having to worry about a custodial partner like Gemini.
When we inquired today if thought Gemini issues might get resolved before on chain payments, and the answer was probably not.