Wi-Fi calling shouldn't be a battery drain at all, if anything it's the opposite, simply because less power is required to connect to a Wi-Fi point a few tens of metres away than a phone mast hundreds and hundreds of metres away. I can go 5 or 6 days connected to Wi-Fi calling without needing to charge my Pixel phone, I simply disable the mobile connection as get an appalling signal at home, so it remains on Wi-Fi Calling (unless I'm out of the house) and it hardly drains the battery, much less than the cell signal.
You need a Wi-Fi access point set up for power saving using U-APSD, all modern access points will support this. All good smart phones will offload the Wi-Fi calling VPN tasks to the Wi-Fi stack, so the phone remains asleep, with the Wi-Fi chip handling the house keeping tasks to keep the VPN alive and respond to incoming calls, all without needing the phones main CPU doing a thing.
To the OP, you may need to test with your mobile signal turned off, simply put your phone into flight mode, then just enable Wi-Fi.