Your calculation of your maximum contribution is correct.
"Does it make any difference if part of my contribution would be made after my October 20 birthday?"
No. You have until April 15, 2027 to make your 2026 HSA contribution.
If you contribute $7,312.50 and your wife is HSA eligible the entire year, she can contribute $2,187.50 plus a catchup of $1,000, a total of $3,187.50.
