Depressed boyfriend pushed me away, how to help?

My boyfriend (only 5 months, but it was very emotionally intense) finally pushed me away for good. I broke it off with him on Tuesday, stating I was not abandoning him, but I was giving him the break he needed so he could work on himself.

He has had an extremely traumatic past including the violent deaths of his parents, repeated cheating by SOs, and continual failures with his career. He also suffers from very bad sleep apnea, which he has left untreated. He is 31.

Our relationship started wonderfully, but about 3 months in he started going downhill after starting a new job. His job turned him into a zombie. Every day when his alarm would go off he'd wake up and say "****, I want to quit my job." It was sad.

We have had very intimate conversations about his depression. He has admitted he is depressed, and has also admitted to self-harming and suicidal thoughts. He says the death of his parents haunts him, and he feels lost in life and a burden to me. He kept saying things like "I can't love anyone anymore," "Why do you want to date someone who works the job I have?", and "I don't think I'm meant to be in a relationship, ever." He still called me every single day and seemed happy to see me when we did, but... he was always unhappy, and kept repeating these comments to me. I once said "A relationship should make you happy, not stress you out. Do I stress you out?" And he didn't have an answer. I felt terrible for being a source of pain for this man.

Finally... I didn't know what else to do. I wrote him a heartfelt letter explaining my love and concern for him, and telling him that I was letting him go. He texted me and said he understood, called me amazing for putting up with his "depressive self," and apologized for being a horrible person. This happened on Tuesday. He is not seeking any treatment, just trying to figure it out on his own.

OKAY, now for my questions. I told him I was not going anywhere, that I will remain here as a friend should he ever need me. I texted him yesterday simply to say "Hi, thinking of you, you know I'm here for you, you're not alone." He replied "Thanks, I'm working on a few things, getting a little bit better," then asked if he could pay me to dog sit his dogs in a month while he travels for a wedding. I said of course. His texts are very curt and emotionless, but I understand he's probably trying to avoid anything that I could misconstrue.

I understand our relationship is over, but I don't think he necessarily wants me to disappear. I think he EXPECTS me to disappear - he's said everyone in his life eventually abandons him. I thought about sending him little notes now and again, voicemails, etc., just to let him know I'm thinking of him. Would that be ok? I'd love to do more like drop of small gifts like cookies or a book but that might be too much. Also, would it be disrespectful of me to offer some suggestions on where he could seek professional treatment? I know he won't seek it out but I'd like him to at least have the information. How can I help him without disrespecting his need for space?

Thank you!!