So much sympathy here! (I'm also the "home admin" spouse.)
It sounds like you're not just complaining about invisible labour—you're struggling with mental load (aka cognitive burden): the admin and planning required for a household to function smoothly. It's that neverending to-do list constantly running in the back of your mind (pay the rent, sign those documents, book the tickets, buy new shoes for the kids, clean the toilet…).
It's exhausting, usually falls on the woman in a straight relationship, has been linked to stress, anxiety and depression… and because it's mostly in your head it's less visible than domestic labour that nevertheless tends to go unseen.
Your husband, of course, acts like it doesn't exist or matter. From his perspective, you're constantly stressed out about stuff he didn't know was a problem. When you do mention it, he doesn't see what the big deal is. Why not just do it? Or ask him to do it? (He's always hypothetically happy to do jobs he didn't care enough about to keep track of in the first place!)
At best, he doesn't realise it's not just the tasks—it's the tasklist itself, the planning, the self-reminders and motivation. At worst, he's deliberately feigning ignorance because he knows it's stressful and is relieved that it's on you. It's hard to tell these apart, but either way, it's so stressful for you! :(
I've had limited success with fixing this in my own life. My husband is intelligent and well-meaning but hyperactive and impatient. While I don't have any specific advice, because a lot depends on what works for you and your husband's actual willingness to help, we found our own workarounds that redistribute some of the burden from my own shoulders.