I got a similar setup without joint account.
My wife contribute to our fix cost (rent, flat insurance, internet …) by a monthly wire transfer. I calculate her % contribution based on our net income.
We update her participation annually or after a raise.
For all the flexible spendings (groceries, restaurant, furnitures ), we use the Certo1 Cembra credit card that we split 50/50 monthly. We alternate this payment in a Tricount file and balance it annually.
We do not track any cash payment or foreign vacation spendings.
NB: at the beginning of our relationship, I was tracking every spendings but she dislikes it a lot and the fairness of this work was killed by the sensation she was « in a debt toward me ». Setting up a regular fix payment and a credit card remove all our money arguments.