GPS sucks for home/away.
Why? Well, inside a building accuracy is low, so you can get an update that puts you outside easily enough, and outside your home zone radius without too much difficulty unless you make that radius unreasonably large. Then there’s the whole it may take many minutes to update problem leading to laggy updates.
WiFi isn’t great since many modern mobile phones will turn off their WiFi when in deep sleep mode (not charging, left alone for an extended period of time). Some behave differently, some allow you to turn that off, and some routers handle it better by having insanely long timeouts (hours in a few cases).
Bluetooth seems to be the ideal solution, particularly when done with monitor or even room assistant. Bluetooth has near zero battery life impact (less than GPS by far), isn’t turned off when the phone is in deep sleep, and the choice of integrations gives you significant control.