Here's what I would do:
VACATION - Do not cancel it, and do not work while on vacation. You need rest, and working a few days a week is not rest, it's work. Do not feel guilty. Your startup needs it as much as you. And above all, your number one priority is to your health - mental and physical.
It's a false dichotomy, though. The startup will survive a couple of weeks without you. At most, it won't grow as much (or at all) - big deal. If you're afraid your tech team will burn the house down, don't let them touch production. In a fast-moving startups there's always tech debt piling up. While you're recuperating, let them clean up things, fix issues, write tests, etc - improve the state of things - without pushing anything to production. It's still useful, important work, and it will temporarily remove you from the critical path.
Do not bring equipment on which you'd be able to work while on vacation. If you do get a panicked phone call, you'll feel terrible about not jumping in and fixing things, if you can. It's easier if you just are not in a position to do that all. If you can, leave your phone (or bring a dumbphone instead).
When you do return to work, start by introspecting why you're feeling burn out. Sure there's ton of work and user base or revenue is not growing as fast as you'd hope, but there might be some other reason: maybe you had a nice clean architecture and now it gets all trampled over by several people just rushing to build things? Maybe the people are not as productive a you hoped? Maybe they're not as passionate as you and you feel like you have to force them to work? Maybe they're not responsible/pedantic enough and you feel like you have to clean up after them all the time?
Or maybe your biz/other cofounders just expect you to conjure the solutions quickly, don't understand it takes time to build something that'll actually work (mostly)?
All of these fears and frustrations are normal, but they should not be buried, instead they should be addressed. First, identify the actual point that frustrates you most. If it's something you're not 100% aligned with your cofounders, talk with them. And talk some more, until they understand your frustration, you understand them, and you devise something that'll avoid it. Don't stop talking until that is fixed. Don't bury it.
If the frustration is due to (your interaction with, or performance of) your dev team: first, make sure evefyone's on the same page regarding what's important (ie. tell them explicitly). If you feel they're slow, tell them. If you feel they write buggy code, tell them. It's way better for them to be told explicitly than to have an angry, frustrated, burned out boss (and they can ense these things from a mile off, trust me9.
Then, try to document best practices. Read this for an example https://sivers.org/delegate (and if you need reading suggestion for the vacation, read everything else Derek wrote). Use every problem as an example of how it could be done better. You can start by enumerating and documenting things that could or will go wrong or need special attention while you're not away. Think of it now, document it now, and you'll avoid frantic phone calls while you're on a vacation.
Fix yourself first (vacation), your startup after that (delegation, expectation).
Good luck!