Your manager wanted you to do a job that required more time. You don't have to get into your mental health issues, you can just learn to say "NO". You are part time, that is your committment, you can say you appreciate the offer but you cannot do that particular job.

You have gotten away from your abusive parents. You need to learn how to set boundaries now, you probably never got your boundaries respected by your parents so now you have to slowly learn how to set boundaries and that it is ok for you to do so with out having to explain so much.

((Supportive Hugs))
OE