hi Anonymous,
that is a hard situation. Let me share how I relate to this.
My ex husband was a hoarder also, who, similar to your husband, grew up in poverty and didn't have anything, and had developed the same resistance to throwing out anything. When I started posting here, we were still together (probably 7-10 years ago - I was posting under a different name... "wife", I think). When I would remove dead light bulbs to throw them out, he would wrap them in paper towels and keep them. He had every receipt since the 70s, even for a loaf of bread. And when I threw out ruined, old things he would dig them out of the trash and save them.
I myself am a mild level hoarder (of things, not trash) but it got to the point you are at, with him. He had a den he hoarded to the ceiling and I just ignored it, until I went in there and saw mice nests.
This is the point where I did something a lot of folks here will say was wrong. I waited until he was gone, and I went in there with gloves and bagged up all the mice infested stuff and hauled it to the dump. Anything that had mice nests, urine, poop...chewed on... all of it, I just shoveled up and took to the dump. When he got back, I told him what I had done, and it was because it was a health hazard.
Was he angry? He was... but it was done. I will note I took photos of the mice poop, nests and areas, and it is a good thing I did because he was in denial and said there were no mice, it was not that bad, etc. So I had to text him all the pictures. It was a slap of reality for him and he had to admit it was bad.
I told him he could clean it up/sort it it I would continue to clean it that way when he leaves the house. In the end he accepted my help and told me to go ahead but not show him what I had thrown out.
I do think when it comes to health matters, it requires extreme measures. This is MY house that I bought before I met him, or I might have just moved out. But I am not leaving MY house or letting it be destroyed.
I will also add that we are not married anymore, but the hoarding was not a huge factor in why. Your mileage may vary.
Also in the case of mice we got a cat from the shelter and it kept the mice at bay. But I would only advise doing that if you will love and care for the cat and can manage a litter box etc, or it could make things worse. You can also get feral, neutered cats from a shelter to have outside, if it is allowed in your area.