Let's go back to 2020 first.
Assuming you are both over age 55, your overall limit on a family HDHP, ignoring medicare, is $7100 plus a $1000 catch-up provision for each of you. The catch-up provision can only be put into an account in the person's own name--each HSA has only one owner. If you have a family HDHP and your spouse has no disqualifying coverage, your spouse can also have an HSA, although they may have to open a private HSA at a bank if their employer does not offer one. So for 2020, your overall limit is $9100, but only $8100 in your account or your spouse's account because the $7100 can be split any way you like but the $1000 can only go in each person's specific account. If you did not know about the spouse catch-up, you can still make a retroactive contribution for 2020, up to April 15, 2021, although you have to let the bank know in advance that it is a directed 2020 contribution.
Then for 2021,
Your spouse's contribution limit is ($7200 + $1000)/12 = $683/month x 5 months = $3416.
Your contribution limit is ($7200 + $1000)/12 = $683/month x 5 months = $3416 + ($3600 + $1000)/12 = $383/month x 7 months = $2683 = $6099 total.
Your overall family contribution limit will be $6099 (your limit) plus $416 (5 months worth of your spouse's $1000 catch-up) = $6515. But you can't contribute more than your individual limit, your spouse's catch-up has to be contributed to an account in your spouse's name.
