One of the things I've been doing to combat my recent GM burnout is playing systems where the story is not entirely the responsibility of the GM. It's not the solution for every group, but it's one worth adding to the toolkit of choices.
There are a number of systems that are structured so that players explicitly or inadvertently provide the twists and turns of plot, which takes a really huge burden off the GM's shoulders. Two that immediately come to mind are Burning Wheel and Apocalypse World, so I'll use those as examples for how it's possible to still have an entertaining game while the GM doesn't know what's going to happen next. I won't detail exactly how they accomplish what they do because that's beyond the scope of this question, but I can outline what dynamics their rules enable that make GMing less burdensome.
The overall gist of systems like this is that they give the players a bit more power to determine the course of the game. In the process, the players' input becomes fodder for on-the-spot GM creations, which is far easier to do than the usual pre-planned GM creation process, and the games give the GM tools to make that on-the-spot creation as painless and fruitful as possible. It means giving up some of the ultimate control that the GM usually enjoys, but in exchange what you get is the chance to be regularly surprised by the game, just like the players.
I find that freshness and surprise to be a wonderful antidote to GM burnout.
The rest of this is just what that actually means, using Burning Wheel and Apocalypse World as examples, which you can skip if the above is enough of an answer for you.
Both Burning Wheel and Apocalypse World have a basic GM tenet that you're there to find out what happens just as much as the players are. The systems are set up such that players are more easily able to say, "I want to do Big Huge Thing X," and make it so that they can actually accomplish that in-game if they want to invest effort in it enough. With that, the players take much of the prep work off the GM's shoulders, because they push the game in the direction that they want for their PC by themselves. At most, the GM might have some ideas about where to take things if necessary, but most likely the players will drive the game just fine, and all that's left to the GM to make the players work for what they want in interesting ways, and to surprise them with unintended (but interesting) consequences when they miss their rolls.
In most games this would be unworkable because it would be disruptive to ongoing plots and would often conflict with the other PCs. Both these example games are set up so that they stay interesting when the group has internal conflict, and both give the GM ways to nudge the unfolding story in interesting directions without needing to pre-plan much of anything.
In addition, the games have ways of giving setting-creation power to the players. In both the initial situation and setting are developed by the whole group in a bottom-up fashion ("start small and local, then expand as necessary"). During the game, Burning Wheel gives players a couple tools for adding things that would be advantageous right then: one is a mechanic that lets characters with relevant skills declare facts about the world if they succeed a roll; the other is a mechanic that lets the character conveniently know just the right person they need to find, again on a successful roll. To make it more interesting (and give the GM a chance to add their own bits of interestingness), both those mechanics can at the GM's option give the PCs what they wanted anyway on a failure, but with a GM-added twist that will make their life more "interesting".
Apocalypse World, for it's part, is entirely built around that kind of mechanic: Every time a PC wants to do something that counts as a roll, they either get what they want, sort of get what they want (with specific complications), or on a failed roll the GM gets to make a special GM move that adds complications to their lives (often "bad", but sometimes mixed good and "bad").
Both those sets of mechanics take yet more off the GM's shoulders. They put a little bit of the story development power into the players' hands, at the cost that what they wanted to happen might become inspiration for the GM to do something related but more challenging.
