You are at the lowest point you'll ever be, if your kids are those ages.
You say that he used to be engaged and more of an equal partner? With that background...
People who do things like have a bath and don't think of bathing their own children, are probably too exhausted to do anything and are being arseholes out of self preservation. Being chronically exhausted and having noise sensitivity are symptoms of be traumatised/things that happen after you have been tortured.
With your kids at the ages they are at, and the youngest not sleeping well, it would be normal for both of you to be showing signs that you've been tortured (sorry).
I really really really just encourage you to push through this time and try to hold your tongue a little bit. And relax your standards as much as possible... If you love him, and he used to be able to pull his weight, and he can't, he is probably coming by it honestly. Is it nice? No. Is it enjoyable? No. Is it fairly normal for, in a couple, one person to start to break down under strain before the other one does? Unfortunately not uncommon.
I'm not sure this is a gendered thing necessarily because I know mums who check out as you describe as well, when the kids are at the ages yours are at. People don't talk about it but it does happen.
You're not going to survive this time if you snipe at him. It sounds like you really want to stay together. In which case, keep communicating with him, tell him how you feel, but don't let yourself hate him either.
And my most important point: LET HIM FAIL. Let the children be disappointed sometimes by him. Let yourself fail as well. Do not turn into a rescuer, a superwoman who does everything. That will destroy your marriage just as badly. What you need to do, together, is let the waves wash over you, embrace the suck. Do not try to fix everything or make life run like it used to.