Where does it say that the UK now considers my mother as my family member?

My mother received her residence card but all it says is the following:

EU SCHEME
PRE-SETTLEMENT

She would like to apply for a Schengen visa and if we could prove that she is considered a "family member of an EU citizen" by one of the EU countries, the application process would be much easier.

Well, the UK does consider her my family member, but how do we prove it?

I checked all emails from GOV.UK I could find, I also checked https://www.gov.uk/view-your-settled-status

But I couldn't find anything where it explicitly says that she is my family member, i.e. on what terms she is here.

Do you know where to find it?

The EU Settlement Scheme is not an EU scheme. The name including "EU" is deceptive.

That scheme doesn't use EU laws but UK domestic procedures. That's why the resulting document doesn't show the mention "Family member of EEA national".