Okay, first, you really need to change your mindset about what it means to communicate your needs and boundaries to your employer.
The fact that you're even calling it an ultimatum and feeling like quitting is a threat is a BIG part of the problem.
Communicating your needs and limitations is just part of being a.responsible staff member. And people leave jobs all the time, for all sorts of reasons, so this should not be treated as a threat.
Now, you may have shitty management who are terrible at listening to your concerns and who do treat people quitting as some kind of insult, but crappy management shouldn't change how YOU approach your job, or what YOUR professionalism looks like.
So yes, talk to your management about how your current work conditions are completely unsustainable for you. That's not an ultimatum, that's just responsible communication and that *is* your responsibility to communicate.
Your potential leaving isn't a threat, it's the natural consequence of you continuing to perform in an unsustainable way.
Now, if you do your part to communicate effectively that your limits have been exceeded and that your current situation is unsustainable, then they will either value you enough in your role to accomodate you, or they won't and that will communicate to you that they are okay with you leaving.
If they're okay with you leaving because they expect someone to be sustainably able to do what you've been doing, then fine, you have every right to leave a role that isn't a good fit for your skills and capacity.
Suffice to say, you have clearly internalized A LOT of work bullshit. That's not a criticism, pretty much everyone does it until they learn not to. Boundaries and effective professional communication are a learnable skill. I HIGHLY recommend that you seek out resources to learn how to better protect yourself and better maintain your boundaries within the workplace.
It's not actually your employer's job to prevent you from experiencing burnout, it's your job to communicate the limits and boundaries that are being pushed too hard and burning you out, and their job to assess if you are valuable enough to try and retain.
I've had some staff where I would happily bend over backwards to give them whatever they need to thrive, and I've had other staff who I just waited to get a resignation letter from because I was fine with them leaving.
So if you aren't valuable to your management, then no one will care what you want or if you leave. They'll just be happy that you worked yourself into the ground for them until the end and didn't make too much of a fuss about moving on.
If you are valuable to your management, then they will care about the possibility of driving you out, and you should emphasize this value and negotiated more appropriate work conditions, or a sabbatical, or both.
In business, no matter what your role, you need to think and act like the executive of your own business, a business that has one resource: you, and that resource is subcontracted out to one client: your employer.
Your client (employer) has control over the role, but the executive (you), has control over the resource (also you). Your primary responsibility is to serve YouCorp, not ThemCorp. You have to keep the YouCorp executive happy, and you do that by doing as well as you can while contracted out to ThemCorp. However, if the only resource YouCorp has starts burning out on an unreasonable contract position, then the executive needs to step in and manage the situation with the client, because burnout can ruin the resource.
So approach this situation as the executive of YouCorp, not the subordinate of ThemCorp. You are the only resource you have, you have to manage that resource responsibly.
If you don't know how to think, communicate, and manage like an executive, then learn. As I said, these are learnable skills.
