D.K.
I have flown 3 times in the past 6 weeks. It looks to me like people are still gate checking their strollers. I do not believe they count as one of your 'items' to get on the plane and I do not believe they charge for it. If there is an open seat on the plane, they will often give it to a passenger with a lap child - then you use your car seat. If not, you gate check it or put in in the overhead (if it fits). If you checked your car seat, then you couldn't use it if there happened to be an open seat.
If I were you, I would take a single stroller. Your four year old can absolutely move through the airport quickly enough. Mine was pulling his own luggage at that age, not riding in a stroller. And you will be able to maneuver so much better.