T-Mobile seems to use custom SIP over IPSec. WiFi calling only works when you buy a phone from them. They store something custom in the phone’s firmware. It might be possible to extract the IPSec key and use a modified SIP client to authenticate over HTTPS. Unless if someone has done this already, I doubt that this is happening any time soon.
Other carriers might do something different. After the T-Mobile-Sprint merger, WiFi calling might change, or even go away. They are merging for increased spectrum/coverage, and WiFi was created to solve their coverage problems.