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We keep our cards themselves separate and typically don’t do Authorized Users on one another’s cards, instead preferring to just refer back and forth.
I don’t think it matters what bank account is used to pay off card balances.
However, you and your spouse want to deal with those details is up to you.
A single joint checking account could be used to pay off cards for each spouse, or you could keep your own checking account and pay it off.
The combination of spousal property can be a contentious issue that is probably beyond the scope of this group.