My experience ...
We put 90% of our daily spending on credit card, and autopay full amount each month. (We have never used debit cards.)
having a high balance can drop your credit score, but once it is paid in full does help increase your credit score. (My swing last month was 100 points, due to an exceptionally large credit card bill.)
I’ve never intentionally carried a balance month to month ... don’t want to pay interest and fees. Autopay in full works wonders for that ... the manual process (or old school mailing checks) has much more potential risk IMO. And autopay is processed the day the payment is due ... so if you have funds in an interest bearing account, you benefit there.