I was hesitant to make this post sooner, because I didn't want to share my assumptions, in case they would later turn out to be wrong, so I'm only updating this now that I'm, more or less, sure that my little friend is out of the woods. Please, share this post if anyone ever asks you about this type of problem, and, hopefully, it'll be helpful to them.
Mantle collapse can, indeed, heal, but not the way I expected it to. On one of the pictures that I posted earlier (
drive.google.com/file/d/13JWa8dCidhvo6565weenXGmSTgbwQo_K/view?usp=sharing ) you can see a small portion of the snail's internal part sticking out after I'd initially pushed the bigger portion in (I imagine the lung would've been squashed otherwise, and was definitely constricted). But that small part seen on the picture just kept slipping out, no matter what I did. I expected it to grow back in if it stayed inside longer, which, in hindsight, was a mistake. I realised the mistake when I saw some new growth near the opening of the shell. I'm not sure how to describe it in English; I think cuticle would be the correct term. It seemed soft and fragile, so I immediately stopped my daily attempts of gently pushing the mantle back in. I didn't want to damage that new thing. I wanted to see what would happen and was a bit hopeful, because, to me it looked as if the snail's body was trying to repair itself. And that's exactly what was going on. Fast forward, about two weeks later the soft part that should be inside the shell was entirely covered by the new growth, and it seemed to be getting thicker and stronger every day. The shell doesn't look whole now, because it had been fully formed before. The new part looks more like an extension of the old shell, and it seems quite hard and solid. Pasi9 was right, after all!
A week or so ago I, finally, decided to take a risk and put the snail back into his regular tank, and he's been moving around freely; the mantle stays firmly inside the new part of the shell.
Maybe it will help someone one day, so I'm going to describe how I was taking care of him when he was healing.
1. I put him on a new clean sponge, which I always kept wet and covered it with a transparent plastic cover with holes (a small plastic box would be just as perfect, so long as the snail has no way of escaping and there are holes for ventilation). It was rather small and just high enough for the snail to be able to move around a little and crawl upside down, so that his shell just lay on the sponge without tugging him down (he spent most of the time upside down, even when he ate).
2. I cleaned the sponge and the cover every day with plain hot water, because I was concerned about the snail getting infection. I changed the food and calcium every day, too. Sometimes twice a day.
3. Daily warm green tea baths, shallow, so that it wouldn't get into his breathing hole.
4. The enclosure was small and became dry pretty fast, so I had to spray it a lot. At the same time, I tried my best not to bother the snail too much and let him rest and heal. I imagine, moving him too much could have undone some of the progress potentially, but he seemed more relaxed when everything was soaking wet.
5. I gave him a lot of various foods that he likes in small portions (because there just wasn't enough space there). I made sure he always had fresh food, especially his favourite zucchini peels, carrots, some sweet fruit treats, etc. I know that some snail owners aren't so lucky, because ill snails often refuse to eat. Thankfully, we had no such problem.
Despite the new piece of shell growing, I did not notice the snail consuming more calcium than before, but it was always there for him (limestone flour and powdered cuttlebone).
Now he's back in his old tank. I temporarily removed the substrate and replaced it with a thick foam rubber padding. I doubt he can get an infection now that his internals aren't exposed, but I want to be on the safe side for a couple of weeks. He was never particularly interested in any substrate, anyway, he prefers to hang out on the walls or on the cover upside down.
Some new photos (you can actually see where the old shell opening used to be before):
He can finally move around in his old, large tank with no trouble, even when the shell is pulling him down:
