Hello, and thank you for using Apple Support Communities!
Based on the details you provided, it sounds like you could use some clarification on the Adaptive Noise Canceling setting on your Beats Studio3 Wireless headphones. I can help.
Check out: Set up and use your Studio3 Wireless headphones You'll see a section near the bottom of that article titled, "Turn Pure ANC on or off." There, it states Pure ANC turns on each time you turn on your Beats Studio3 Wireless headphones. This will be a setting that you will need to turn off each time, if you wish to do so. There is not a way to save the setting.
It was a pleasure answering your post today.
Take care!