Given that insulin seems to be the main culprit in metabolism dropping while dieting, I would take care to look into studies on the specific sweetener in your drink and verify that it does not create an insulin spike when consumed.
A drop in your metabolism would make you feel bad on your fast and reduce its effectiveness.
Good luck to you.
Just look at the back label. Some energy drinks are just glorified overpriced sparkling tea with vitamins. And yet I still buy them when I’m having a hunger urge as it makes me “feel” like I’m eating/drinking something special and helps me continue on fasting.
As far as autophagy? Who knows? I wouldn’t drink only those all day, but one that has simpler ingredients and not tons of artificial sugar, why not as long as it helps you continue to fast. Just my opinion and not backed by any research though.