From my limited experience, much of which confirms prior comments here on staying inside the park, the private campgrounds outside the park are the best compromise. We are going in Aug \ Sep '21 and this is the 2nd time I've planned the trip. Tried to go in 2020 and there were more barriers to climb over than I can delineate here.
This year, we are staying at firesidejacksonhole.com for Grand Teton and yellowstoneholiday.com for Yellowstone. Yes, Fishing Bridge Campground, the only in-park campground with full hook-ups, was/is still closed to reservations for 2021.
It's unfortunate to be outside the park but that's the trade-off unless to you want a sub-30' rig with a gen set and solar for good measure. Tried to convince my wife to go for the Unicat but she didn't even bother to respond.
From what I have seen with the rush to RV camping, I would not travel without reservations, especially to Yelllowstone. Best of luck with it!