Maximum HSA contribution

I am 65 starting with Medicare in Sep. my wife is 64 starting Medicare next year in Nov

we are both retired and have a High Ded healthinsurance through the marketplace

I have an HSA, which I carried over from work and my wife does not have an HSA

 

we have been axing out HSA contribution the last few years, and I like to continue even into next year until my wife goes on Medicare,so I opened a new HSA for her- for this and next year

I want to make sure I am maxing out our contributions, and here is my math

For my HSA this year : family contribution max 7750 plus 1x catch up 1000 = 8750, prorated for 8 months =8750/12*8 = 5833;  for my wife's HSA, Individual max 3850 plus 1000 catch up = 4850, prorated for 4 months of year = 4850/12*4 = 1616.  Then Next year - (lets assume same limits as 2023 for the math) - my wife can contribute max Ind 3850 plus 1000 catchup = 4850 prorated for 10 months = 4850/12*10 = 4041

is this correct or can next year calculation be based on family contribution max (even so I am on Medicare?

I assume the catch up contribution only applies once to the HSA owner, and cant be 2x1000 for both of us?

 

thanks for any help validating