PSA: until you've experienced burnout, you are likely to underestimate how long it takes to recover. It's not a couple of months, it's 6-18 months for partial recovery, and maybe 3 years for full recovery (all depending on how bad it gets). The company burning you out will almost never support your recovery, mostly they'll drop you when you stop being productive.
Nobody in business cares about your health but you, so be your own advocate, or suffer the consequences.
I don't say this with any particular bitterness, more that this seems to be generally how it is, and you should know that your loyalty to your team and the people that employ you is just not worth the damage that you are doing to yourself, because that loyalty will not be there for you at the end of the process, and healing takes a surprising amount of time.
To put it in ecological terms, your health needs to be a sustainable resource for you. There is no safety net.
Daniel
Bo Jeanes