Same situation as you are but from less-known, less-prestigious Master program and school. From my point of view.
Yes, you can apply to top Master Quant/Fin program with that MA Stats can give you some advantage, BUT it is not optimal idea because you are already have the degree from top STEM school with UCB Stats is like top 5 in the US, the school also well-respected in many industries so why not utilize it.
From your past post, it seems you are admitted for this Fall. So my advice is try to find research position and contribute to many papers so that your name can be found on google scholars (this is the best because a guy I know also MA Stats contribute to 4-5 and got offer for MLE at unicorn right after graduation), gather a team to compete hackathon, datathon, risk competition, networking event and most important is connections and interview preps (study, eat, sleep with it if your goal is toward trading/quant firm/hedge fund). Try your best to fill in any gaps and have every achievement/accomplishment appear on your Linkedin/resume.
In conclusion, my advice is from my failure in my past Master program and by saying this, I want to prevent anyone to fall into this problem as I did. If my idea/advice does not make sense, just ignore it and someone will definitely help you out. Wish you the best