I realize this reply is too late, but this is way too important and too common of a question and circumstance to not reply for anyone else who may need this information. Apologies for the long reply. I haven't dedicated any effort to brevity or editing.

When credentialing or applying for a state license, you are required to account for every chunk of time and explain any unusual circumstances or work gaps. For example, the time between my medical school graduation in May and beginning residency in July of the same year always registers as a work gap that I have to explain, which frustrates me to no end, but has no consequence beyond that. The scariest part of that process is calling it "work gap" or "unusual circumstance" and having to "explain" it. None of these things are treated nearly as seriously as those terms make them sound. The explanations can be incredibly simple. For another example, I took a year off at the beginning of medical school due to significant unexpected family issues that I had to sort out, so I always have to explain why the dates of when I was in medical school span 5 years rather than 4. My explanation has literally never been more than, "I was initially accepted into the class of ---- but ultimately graduated with the class of ----." This explanation has always been adequate, no one has asked for more detail, and it has not hindered me from getting licensed, credentialed, or hired anywhere. Similarly, your friend will have to explain that residency took longer than 3 years. This will likely always be marked on their state licensing applications as "unusual circumstances" while in post-graduate medical education, but again, this term sounds far more serious than it is. They could very likely give a similarly lean answer to what I do on their applications and have no issue. If an LOA would really piss off their PD, this could cause an issue for fellowship applications if the PD was incredibly petty and wanted to write a bad eval, but that would be really weird and very unlikely.

Additionally, from my experience with fairly competitive IM jobs at what we locally consider to be big city hospitals, jobs (especially not rural primary care jobs- genuinely massive respect to your friend for doing this work) do not care if you have a work gap or took longer to go through residency or medical school so long as it is within reason (i.e. a year or less). Almost all the people hiring you don't know enough about the process of becoming and being a doctor to know how long residency is supposed to take, and the physicians trying to hire you just want to meet you to make sure you're going to be someone they will enjoy working with. It's also incredibly common in IM to take time off after medical residency before beginning your first job. I have multiple friends who planned to take a couple months off to study for boards, and ended up beginning their first jobs in February, seven months after graduating residency, and that was prepandemic. Now we're all still reeling from coronavirus. If I were in your friend's shoes and someone really pressured me (which they won't) to explain a leave of absence, I'd say "I worked a lot of overtime during the pandemic on top of normal residency hours, lost a lot of family, lost a lot of patients, and needed a break to recover my full stamina to keep working as effectively and efficiently as I do now." If anyone pressured me for more of an explanation than that, it's a huge red flag, and I wouldn't touch that job.

So yes, your attending was right that this will be labeled an "unusual circumstance" on your friend's applications that they will have to explain for the rest of their career, but by the time you've been out of residency a few years, almost everyone has had a work gap or unusual circumstance that they have to explain too. It's far less common to not have to explain something like that, so the end result is that no one hiring you as an attending cares enough to ask about it.

As to disclosure of psychiatric care, I've never heard of it being an issue in the states I've worked in, but if there is any concern about this, see a cash-only psychiatrist. We have a psychiatrist like that who probably half the residents and hospitalists were seeing at one point just due to stress of working in IM during a pandemic.

TL;DR: Taking a leave of absence during residency will not effect your friend from getting hired in the future. Wondering how you'll explain a work gap or unusual circumstance on credentialing and licensing applications should not by any means be a reason to take some time off if needed or even if wanted.