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If you have a credit card with a $25,000 limit, that limit counts against your total even if you are not using it. For example, if it is determined that you can sustain mortgage debt of a maximum of $400,000 at current interest rates, you will not qualify for that amount because you also have an open credit card with an available balance of $25,000 at a significantly higher interest rate.
I have bought and sold over a dozen houses, my credit has been shit and I repaired it, and I have worked for a number of insurance related tech companies that evaluate your credit. What is considered when evaluating your viability as a borrower is your debt exposure. Credit cards are pre-approved debt. If you have $100,000 of combined available credit on credit cards, then you might as well be $100,000 in debt. This is especially true if you got these cards while you were in a higher income bracket than you are currently. If you had a nice job paying $125k but had to move and now make $95k, then those cards might represent a debt burden you might no longer be able to carry. That is a huge ding when being evaluated for credit.
EDIT: By the way, most people also believe that only the outstanding balance is counted. That is true for loans but not for credit cards.