Family Sharing Setup - not recognizing correct email for child setup

My daughter’s Apple ID that she uses for her phone is an @gmail account. Of course, when she became an apple user she also had an @icloud account created for her. This account is not used anywhere on her phone. When I look at her apple account page it shows her @gmail account. Her contact card only shows @gmail. Her media & purchases are all set up under @gmail.

When I send her a family sharing request and she accepts, I get a notification that @gmail has accepted. However, when I got into her profile on family sharing, it is showing that her @icloud email is linked to the family sharing account. This is mirrored on her phone. I have tried inviting her via email, text, and air drop with the same result.

This is preventing her from having access to shared purchases and most importantly, our iCloud storage for her phone backup. It says she has access to my iCloud+, but because her phone is set up under her @gmail and not @icloud, it will not actually give her that access. However, I can still manage screen time, Apple Cash, purchases, etc through the family sharing account.

How can we resolve this? I’ve researched and I am completely stumped. Thank you!