British citizen travel to EU with EU ID card

Hi
My daughter's passport expired, whole renewal process taking ages and could not arrive before our departure. All of use having dual nationality, however with renewal needed to send both passports UK and EU. We all have EU ID cards. I'm just wondering if my daughter will be able travel to and from EU using just ID card, rest of us have valid UK passports. We never applied for EU Settlement Scheme, as we obtained british citizenships few years before and never needed. My daughter born in UK we already applied for passport, status shows approved but did not recieved it yet. Is she allowed to travel using EU ID card as British citizen

The new passport might just arrive in time ....
First, you can leave the UK on any valid ID travel document so EUID card can be used certainly for outward travel.
Was daughter registered as British? Or has dual citizenship through birth?
If registered you could take the certificate with you and show it on your return to the UK.
If dual through birth perhaps take your naturalisation certificate and child's birth certificate showing your name as parent.
No personal experience of this but note that a British citizen has automatic "right of abode" in the UK and cannot be refused entry - it may take at bit longer at the UK border. Note that certificates are not travel documents and won't be recognised by carriers - these are only to help with entry to the UK. Unfortunately there's no easy way to prove you are British, unless you have a valid or even expired British passport or lacking that some documents showing registration/naturalisation.