I completely agree with earringsandlipstick, your actions really do not read to me as inexcusable in the slightest. Once per month contact is hardly smothering her and blowing up her phone 24/7. It's minimal contact that at the very least shows their mentally ill daughter that they are thinking of, and care about her.
I'm only 27, and I'm close to my mum now. She's very actively involved with my toddler. We are good. It wasn't too many years ago I was 22, on anti depressants (like the majority of my friends), smoking weed daily, coke and md more than I like to admit, hating on my parents, some of my friends were self harming. I thought my entire family just didn't get me. If they'd all totally backed off when I was awful to them and said I hated them all then I'd be pretty bloody lonely now! My parents didn't know how to handle it, the amount of arguments we had when I said my mental health was in tatters and they berated me for being on drugs. None of us handled it right, there's no guidebook for these things, but at the end of the day I knew they cared and were there for me.
All I can say is I was in with a group that all had mental issues, substance abuse, one of our closest friends in that group committed suicide when I was 21. Well I'm now 27 with a lovely toddler and a baby on the way. Some of my friends from back then are the same, some are happily married, some are only now doing university and making a career for themselves, not a single one of us is as we are back then. I remember one of my friends moved out of her mums house and blocked her off everything during that time and I saw her put up an Instagram post the other day of her and her mum hugging at her baby shower.
So no, coming from someone with some experience with these difficult relationships, I would not now stop contacting at all, especially after an overdose. Keep maintaining enough contact to show that you are still there despite it all, but enough space that she doesn't feel smothered. Once per month sounds more than reasonable