My (33m) girlfriend (35f) is battling depression and I don’t know if she’s wants me to stay or leave?

I’m not very good at writing so I apologize for any grammar mistakes or rambling I may do but hopefully someone can help in some way. My (33m) girlfriend (35f) is battling depression and I’m absolutely clueless what to do. We’ve been together about 6 months but I knew her for about a year before that. We became really close before we got together so when we finally did it was effortless. We went out regularly, went on trips, and genuinely connected in a way that I’ve never experienced. I’ve seen what this relationship could be and I want that so badly. I truly believe she loves me and I know I love her. The problems started about 2 months ago.

She has a lot of things that she hasn’t truly processed and it finally started hitting her. A few months before we got together she lost her father. Her father had his own demons and their relationship was not a good one. From what she’s told me he had a pretty bad drinking problem and was in and out of jail. His addiction led to health problems that eventually took his life. I don’t think he was ever physically abusive but he neglected them and treated her and her siblings more as friends than as a father. There’s a number of other things that I’m not getting into just know that they were not on speaking terms for a number of years leading up to him being hospitalized and their last conversation before being hospitalized was a fight. She knows that he loved them deeply but from what I’ve gathered he just didn’t know how to process things well and hurt a lot of people because of it. Her mother walked out when she was young and you can count on one hand how many interactions she’s had with her since then. Her mother is also an addict but there is no relationship between them at all. She holds tremendous love for her father but also a tremendous hate. I believe she also carries a lot of guilt because of the hatred she has towards him, she thought she’d have time to reconcile with him but unfortunately that never happened. Once these things finally started hitting her she hasn’t taken it well.

She slowly started pulling back. We stopped going out. She started shutting down conversations. Generally just being cold towards me. She told me her depression had came back and I’ve tried everything I can think of to try to help. I understand how depression works because I battle it myself. So I never raised my voice, never argued with her. Constantly get her good food, flowers, and a number of other gifts. She used to laugh and enjoy my company but now it seems like she could care less. I told her about how much Reddit could possibly help and she said she was going to look but I know she’s lying. I’ve talked to her deeply many times about what’s bothering her and begged she seek therapy but she always shuts it down. I asked her about things about 2 weeks after it started hitting her if she was alright and she told me about a lot of things. Said she doesn’t know if it would be better if I stay or go. I told her I wasn’t leaving unless she wanted me to and she said she didn’t want me to go so I stayed. Fast forward to yesterday. I’ve been battling for a couple of weeks with myself because I didn’t want to add anything else on her but I had to know. I asked her yesterday if she wanted this relationship. If she actually wanted me. If when we talked about this earlier she was trying to be nice so she didn’t hurt me. She said she wanted me but also she doesn’t know. She said it’s not fair to me because she can’t put any effort into this relationship right now because all her energy is going to just getting by. I suspect she feels guilty about that answer so that’s just another thing added to her plate. I feel guilty for bringing this up and giving her something else to stress about. I still don’t know if she’s trying to tell me to leave without telling me to go or if she wants me to stay and help her through this. I don’t want to stay and her resent me for it. I don’t want to leave because she might see that as just another person who abandoned her. The thought of giving up the best relationship I’ve ever been in terrifies me. I feel absolutely gutted by all of this and I couldn’t live with myself if I left and something happened. So if anyone has any suggestions I’d truly appreciate it, please help?

TLDR My girlfriend is struggling with depression and unresolved trauma from her parents. She’s become distant and says she wants me but doesn’t know if she can handle a relationship right now. I don’t want to abandon her, but I also don’t know if staying is hurting both of us. I love her deeply and am lost on how to support her without pushing her. Need advice.