Edit 2:My question is not a duplicate of this question: Should I tell my recommendation writers about my self-studying since graduating? Should I also mention my illness and depression? because I am asking about how much of the details of this setback should be discussed and in what manner with potential supervisor/ admission committee in the interviews not to referees. So, kindly reopen this question.
The question asked here is an extension of this question: Should I mention about the time wasted (6 months) due to depression in my CV when I will apply to PHd programs
Edit 1: I am applying to UK, France and Denmark.
Very brief overview of the situations that happened from Jan 2021 : I am living in a 3rd world country. I completed my masters in math in Jun 2020. Then I wanted to study some additional topics before applying to programs in Europe. So, I took a yearlong break and went home. I studied fine until Jan 2021, then constant verbal abuse by my father started and occasionally by my mother (they earlier also used to verbally abuse me, but I didn't do my bachelors and masters in my native city, so there was less impact for me).
I was admitted to a mental hospital for 10 days in Feb and misdiagnosed with schizophrenia (I have depression). Verbal and emotional abuse continues, and again I was admitted to a different hospital in March for 11 days, diagnosed with depression. Verbal abuse again continues after some days of me being discharged. So, I moved out, taking on a part time job to sustain myself in a different city on 1st of July and I have been learning some new math topics alongside. I am thinking about suicide since March 2021 but postponed to try for one more year to get a PhD position, as learning and doing math is the only thing I like.
(Reason of verbal abuse: parents wanted me to do full time job and not math research so that I can settle early and also wanted me to take a career like medical doctor or engineer which earns more and takes less time to settle). I could only study 1 month of math in these 6 months.
From August 21 to now: I am learning new math topics alongside my part time job and have applied to 3 Phd programs so far. I have interview calls: one from a potential supervisor and one from an admission committee of 4 professors in February.
In my CV I just wrote that from February to July 2021 I could not be as productive as I wanted to be due to personal reasons.
How much should I mention the exact situation I faced and why I couldn't be as productive as I wanted to be if asked (if not asked I will not tell anything about it) in interviews for PhD positions and in what manner to paint a positive picture?
I really need advice.
Depression is in check now as I am away from my parents and take medicine regularly and reading self help books( Good therapy is not available as I live in poor country with not much health infrastructure).