Equal treatment at different ages.

Whilst I agree that you should follow the parents’ rules I don’t agree with their rule. Making children always equal can breed resentment later on when life intervenes and one perceives they have less than the other. Learning to celebrate others and enjoying their happiness or achievement is a good life lesson.

If the 6year old wins a competition at age 10! Or any other age,would he/she be rewarded? If the answer is yes then surely that is equal.
They aren’t equal. One has won a competition and the other hasn’t.
I suppose you’d better check though or you may not be flavour of the month.
I still occasionally mention that my sister got a doll on my birthday (as did I ) because she was too young to understand. I got the message that my birthday wasn’t special.
We are all best of friends now of course!

do nothing without fully discussing with and getting approval of the parents.
respect their rights and their role.

I would congratulate her and take both grandchildren out for a little treat. I see that as being fair to both of them. What you propose isn’t, imho.

Does the 10 year old need a financial reward from you, wasn't there a prize for winning the competition anyway?
I'd just buy her a congratulations card, and if circumstances allow take the 6 year old to help choose it.
Or make a card together for the older sister.
Don't do something that you already think will cause trouble 😕