It does shut off eventually, I have that same Android Auto adaptor, a Radar detector and Dashcam all connected and they stay on for a while. If I had to guess I would say 30 minutes or so.
I have not had any battery issues.
Waze and Radar detector here.... That said, I detected a cop in my area using Laser last night for the first time.
And he was on the Waze app too. So that would have saved me if I was going the other direction.
I use Waze mostly for now,
I have had this on in my cart for a few days, trying to decide if I want to get it. Lots of good reviews and tests online.
Radenso DS1 Driver Assist Device
https://www.amazon.com/gp/product/B09JT4T34R/ref=ox_sc_act_title_3?smid=AH05JFUR0L9NT&psc=1