Deductions & credits

Thank you for your explanation regarding HSAs. My second question pertains to the catch-up contribution of $1,000 available to individuals aged 55 or older. Both my wife and I are over the age of 55. However, under our family HSA, the catch-up contribution is only $1,000 total. If we were to each have our own single HSAs, would we be eligible to contribute $1,000 to each account for a total catch-up contribution of $2,000? Am I correct in this understanding?