Is adrenal burnout a bona fide condition? And what's the treatment for it?

Semantics. Sounds like you've had different as to your q. Just wanted to point out the reason for the differing opinions is prob bc you used the word 'burn-out.' when ppl say burn-out, they refer to 'adrenal fatigue, ' which most mds agree does not exist. But if a dr thinks u r asking about adrenals not working, then yes, adrenal insufficiency does exist, but doesn't happen bc it burnt out/got tired.
Addison's. Yes, there are varying degrees of adrenal insufficiency and hypoadrenia. Addison's disease is complete failure of the adrenal glands and requires replacement medication for survival. The cause may be infectious, autoimmune, or iatrogenic with long-term steroid administration. We also see varying degrees of adrenal insufficiency that do not qualify for complete failure.
No. There is no such thing as adrenal burnout, adrenal fatigue or "sluggish" adrenals. Therefore, there is no treatment. Beware of those who would sell you adrenal supplements. Even though they contain "natural" ingredients, they can be dangerous. They can raise your blood pressure and cause high levels of potassium in the blood.
Yes, steroid s. It sounds like you are referring to adrenal insufficiency. There are a variety of conditions which can cause the adrenal glands to fail to produce stress hormones that are important in the regulation of multiple body processes including maintaining a normal blood pressure and salt content in the body. The treatment involves replacing the hormone & at times treating the underlying cause if possible.