Synchrony is the big backer of most store cards, but Apple's card is quite different. Synchrony has a track record of poor service and consumer complaints, so I don't see Apple going this route. A BIG mistake if so.
Many years ago, stores ran their own financial service divisions (think Sears, JCPenney, etc.). it was only recently that these operations were outsourced. Apple running their own financial arm is not unprecedented.
Besides, IF an Apple Car is coming, Apple will need a financial offshoot anyway, like most auto manufacturers. GM Financial is the best example -- they fund many GM vehicle sales, but also have their own Mastercard and Visa -branded credit cards.