Hey Luca!
Fair is not 50 50 when the gas tank is not the same. Longer hours mean less energy and fewer usable hours at home and so the person who gets home earlier usually runs point that day. Count commute and recovery time, not just clocked hours, because showing up exhausted still counts as a cost. People also inflate their contributions in memory, so write it down where both of you can see it.
If money is the reason one person works those shifts, spend some of it to buy time. Rotisserie chicken and a once a month cleaner are cheaper than resentment. Assign ownership by area for a week at a time instead of slicing tasks into infinity. One person owns kitchen outcomes this week, the other owns laundry and floors, and you swap next week. No minute by minute scorekeeping, just outcomes by Sunday night. Have a default rule for surprises, like if a shift runs over, the at home person handles dinner and bedtime minimums.
Fixed windows beat endless exceptions. Strip devices to a few apps and no notifications, then expect pushback for two weeks. Consistency is the only fairness they believe.