The short battery life is not surprising with wifi. The camera is continuously sending out a signal, whether you are shooting, to maintain the connection. Also, I've found trying to work with a phone rather than a laptop seems to tax it a bit more because the phone's signal is weak by comparison. A laptop naturally has a stronger signal. About four months ago, I was working with the 5D4 for a prep day in the studio while we set lights and background. I connected the camera directly to the laptop via the wifi and it lasted a good 6-hours while I took test frames, etc. I did turn the camera off when we broke for lunch. Oh, one caveat I just thought of. I used the battery grip, so I guess you can halve that time.
Every time you use added electronics to do something such as run the wifi or use the GPS, you drain more of the battery. With an iPhone, they tell you to turn off wifi and bluetooth to maximize the battery.