Pointing out that OP shouldn't have had the baby is just cruel and not constructive.
OP, you sound at the end of your tether, but as you say, all three children are equally important and your eldest two are showing you just how much they need you right now.
You need to 'fake it til you make it' I think. Prioritise your relationships with your sons. Act like you're enjoying their company even though it's hard. Set them up to win - I think that prob involves getting out with them but making it an easy and undemanding activity - my eldest is the same age and I was surprised how much fun he/we had with a frisbee he was given recently! Five mins walk to the park, doesn't matter if they're wearing the wrong clothes as it's hardly a day out, and then actually engage with them while you're there. Something like that. Make it as easy on you as possible. Swimming can also be good with those kind of age gaps IME, and allows for a bit more 'play' than tired mothers can sometimes manage and a bit more reassuring physical contact than busy big boys are otherwise up for, but faffing about getting changed etc may feel beyond you just now and fair enough.
I would do whatever you can to set yourself up with baby plus one older child as often as possible (and then actually actually something with them - even just prep a meal together or whatever) - if not your ex, see if you can fob off one child at a time on your partner, your family, your/their friends. If your partner is serious about you, he needs to show it by making as big an effort as required with all of your children, and if you're serious about him, you need to show it by trusting him to cope.
Bollocks to all the reward charts and fines and sanctions. They don't work for all kids at the best of times, they won't work for kids who are currently feeling unwanted and unloved and anxious about their role in the family - on top of all the additional angst even the best-supported ND kids often experience just by having to navigate a very NT world.
I know you love your children and are just totally burnt out. But with children, ultimately the message they receive is the one they internalise. I am 100% sure that your children are currently receiving a message of rejection and dislike, just as all the posters on this thread have picked up, and even though it feels like you have nothing left you need to find a way of powering through and fixing that. It's not fair but it's motherhood. 🤷🏼♀️
I think the breastfeeding thing is a red herring. No need from my POV to wean or reduce feeds to allow DP to take baby out for a long time. 8mo babies can go ages between feeds if they're away from their mother (nobody would be stressing about baby going 8+ hours without a feed overnight for eg), they'll just make up for it when they come home again.