I mistakenly clicked the “capture payment manually” button instead of capturing the credit card for payment. Will the credit card be charged?
If you did this in a draft order then no, the manual button is telling Shopify you intend to take the payment offline somehow. Like cash or cheque. So no money will have moved at this point!
Is it still possible to capture the payment via credit card or do I have to
call the customer and ask for the card information?
You might be best off recreating the order and sending it to be paid as intended and then voiding out the incorrect one.