I'm running a couple of messenger clients and a web browser (Fennec under Android App Support as the native one is sadly a bit behind the times currently) all the time. The only thing I've noticed to eat a ton of battery is having wifi enabled when outside the range of my own networks, it seems the scanning the phone does in the background to look for known wifi networks is not energy efficient at all.
And, yes, I often turn off wifi. I never go over my Data limits and 4G/5G is much more efficient for some reason.