Hi OP. I've joined Mumsnet to reply to your post as the way you're feeling really resonates with how I felt about my firstborn's sleep. I don't know if any of this will work for you, but I wanted to share.
Firstly, it is so incredibly challenging. You are doing so much to help your baby, and you are doing an incredible job. I know those feelings of not being enough, of baby hating you, and they are powerful. But you are seeking help and you care, and those are really important things.
My first baby didn't sleep 'well'. Night or day. He'd wake up every 45 mins at night. Daytime naps were a battle. For the first year (and then some but the first year was the most intense) I'd fight and fight to get him to sleep. He'd go and his eyes would pop open again. Or he just wouldn't sleep. I was desperate and worried about him, and I was desperate for space. I would get so angry. I was so anxious and keyed up and I could never sleep when he did sleep in the daytime, and nights felt like constant, shocking torture.
And, though this may not always be the case, and of course if you're worried about his health and development it's worth checking in with your HV/GP (though that can be easier said than done at the moment), my son is completely and absolutely fine. No-one was worried about him because he hit every milestone and was happy and healthy. I however, was a mess, and unfortunately a lot of the advice out there made me worse, including what HV's said, like stuff about making a rod for my back/creating 'bad habits'. My baby who was fed to sleep at every single stir because it was actually easier for me than any alternative now, and has for a long time, gone to bed with his dad for naps and night sleep and been settled only by his dad, and even slept through the night (unthinkable only a year ago) without even a whisper of me. I wish I could travel back and smooth all the stress about it off me.
Really what I related to is how you're feeling in your posts. I would do everything to help him sleep. The days he slept 'better' I would go through every tiny detail of our day. How much sunlight. How much he fed. How many times I'd blinked. I felt it MUST be something I was doing, and that I was damaging him and failing him. I hated myself for getting the most angry I've ever been with the thing I loved most in the world.
Now I'm 6 months into our second (great sleeper until 4 months and it's all gone a bit more challenging since though I haven't changed - he has, as he will) I've realised it was just the way my first son was. And so many babies are. And there's all this stuff about sleep, because when you're tired, and a new parent, and your whole life has changed, and you're desperate, sleep is big business. Plus, and I think this more, when you become a parent everything has changed, and sometimes there's a feeling, a need, to control things you just cannot control, because - I don't know your story but - however much you wanted to become a mother of however much you love your child absolutely - it is a massive transition from who you were before to who you are now. And of course you want to do everything right by this incredible and important new life.
So. There are some things about sleep which helped me. I try and take a pinch of things from here and there and try and listen to what instinctively makes sense to me (again easier said and it is so different now I have our second and I'm a different person in relation to his sleep). Sarah Ockwell-Smith and her stuff about ranges of infant sleep and the reason why babies wake so much, and that it is normal, was helpful to me, as was the 'BEDTIME' ideas (to help me feel I was doing something). I decided to choose that way over other ways and it did take some pressure off, to help me feel less of a failure, and it did. It was still challenging though. With my second I've accepted he sleeps when he sleeps. He has to, because I don't have the time to dedicate to his sleep like I did with my first. And he's absolutely ok, and so far there has been really no rhyme nor reason to when he sleeps versus when he doesn't, other than because he's growing and changing. I find it easier to sleep because of this, and I've learned the things I need to preserve my own sleep (eye mask, Bluetooth wireless earphone headband, listening to silly podcasts/music/sleep meditations) and focus on that to help me stay sane(ish).
If you can, talking to someone about how you're feeling about all this might really help, and getting some support for you.
I shall stop this long long post now - mostly I wanted to say you are not alone.