I figure if its running all the time, it will use battery and data in the background, since it will be doing encryption and routing traffic. The last time I used an i2p router on my phone was over a year ago, I was using it to access my Invidious instance, I was using i2pd and had the bandwidth set to unlimited, it was running on public wifi, so it wasnt port forwarded or accessible outside of the LAN, I dont remember exactly what it said it used in bandwidth before I shut it down, but it was less than 100mb, idk what the battery was at before I turned it off, but it ran for about 2 hours that day.