I was wondering the same thing. I often use FaceTime audio to call people overseas so I don't incur long-distance charges. When I tried to call someone today, after installing iOS 26, the FaceTime icons were gone from their Contact page, just as you said.
I actually had to open the FaceTime app and start a new call that way to ensure I was using FaceTime and not just making a call through my cell service.
Now, Bulgarus has highlighted the fact that you can hold the phone icon on a contact page and it does pop up the FaceTime option. I can confirm that this does work, and it is possibly slightly better than using the FaceTime app. However, both options are a massive downgrade.
A third way I discovered is that if you are messaging someone, there is a video camera icon in the top right of the screen. You can hold that, and then a FaceTime Audio option also pops up.
A fourth way is to search in your contacts, find them on the list, and just hold their name. Then a call option pops up, and there is an arrow that allows you to select FaceTime Audio. I think this might be the method with the least friction, but I don't understand why any of this had to change for iOS26.
What was wrong with the old way of doing things?