I would need a heavy-duty extension cord because I would have to run it 60 feet from my garage all the way into my kitchen. I also have no idea how I would actually plug the fridge in because the power cord is hidden way in the back.

That it would be more convenient in the long run if I could backfeed to my panel, but almost no EVs in the U.S. are actually capable of this. The F-150 Lightning that you have is quite unique in this regard.