Oh gosh - don't feel like a failure. You aren't. Not at all.
I had similar with my DC3 - still hadn't regained birth weight by 6weeks, dropped from 75th to 4th centile. DH left when I was pregnant, so I had a newborn, a 2yr old & a 4yr old, and to be honest, I can recognise now I wasn't feeding her enough. She'd feed and fall asleep and I'd be happy the feed was over, so I could rush around and get jobs done/spend time with the big two etc. Whereas the first two bf for a year because I had plenty of time to sit there and feed feed feed all day long.
There is no guilt in bottle feeding. There is no loss of bond. If anything, it made my bond stronger with my DD when I started introducing bottles. When I was breastfeeding, I could do it one handed, so was usually on my phone with the other hand, Mumsnetting or doing the Tesco shop etc. But I needed two hands with bottle feeding, and we just looked in each other's eyes the whole time. It was lovely. It made her an easier baby- she would be put down after a feed and sleep for four hours solid, and she was so happy and content all the time. She went from being visibly skinny to a perfect little 50th centile baby.
If you want tips/advice on bottle feeding, I'm happy to help, but I don't want to overwhelm your thread with pro-formula stuff if that's not what you are after.
But, you're breastfed three kids successfully. You supported other women in breastfeeding- you know what you are looking for here, and you'll have tried all the obvious stuff. Nothing is wrong in admitting "hey, life isn't as easy now with four kids, I don't have the time but used to have to invest into it all, it's not working, and that's ok, we're a different family now, and I need to consider EVERYONES needs".
If you think you & baby might be happier after trying formula, introduce one bottle. See how it goes. It doesn't need to mean the end of your breastfeeding journey.