Do I need to get a UK citizenship certificate for my daughter when I have her UK passport already?

I used to live in Hong Kong until I was 8yo and then emigrated to Australia. However, prior to immigrating I received British Citizenship & a UK Type P Passport under the British Nationality (Hong Kong) Selection Scheme back in the 1990s. My 14yo daughter just received her UK Passport by decent as I applied. We are not living in the UK but in Australia.

But I remain confused between the UK passport and the UK citizenship certificate. So does my daughter need to get a UK Citizenship certificate? I notice that I needed to send my UK citizenship certificate to show eligibility to get my daughter's passport so I'm confused whether her UK passport presupposes that she is now a UK citizen or whether I should apply on her behalf for the UK Citizenship certificate directly. My husband is not a UK citizen but an Australian citizen.

British nationality Hong Kong selection scheme:
https://en.wikipedia.org/wiki/British_N ... prov=sfla1

Your daughter is British from birth, she didn't register or naturalise as British, so she won't have a British nationality certificate.
Her claim to British citizenship is through your naturalisation certificate, her full birth certificate, and your marriage certificate. She needs to hold on to those documents (in original) her whole life to demonstrate she has a right to a British passport as that is the prima facie evidence or her claim to BC - her passport is only a travel document.
Also note that as she is British by descent her future children born outside of the UK won't have a claim to British citizenship - they will need to be born in the UK to be able to be registered as British.