I am so sorry this happened for you. I think your vet was right that it could have been some genetic defect your hamster was born with - and the second one may have been bred the same way. Or - what can happen is there is illness at the pet store and both your hamsters from the same store had the same illness.
If you disinfected everything it is unlikely the new hamster contracted the same condition and it does sound a bit more like a genetic thing by the lack of disease symptoms. A weak heart maybe.
If a hamster has died from unknown causes though and there is a chance it could be infection. Personally I would not re-use wood items, as they are hard to disinfect. Plastic or metal things are easily sorted. Just as a guide for next time to be ultra sure.
I would suggest you get a hamster from somewhere else. And do get another one - you have a lovely cage sorted. And maybe write to the pet shop expressing concerns that there may be illness as both your hamsters died, with no other adverse circumstances, and politely request that you would be grateful if they would check this out.
Sometimes smaller pet shops have better bred hamsters, or you can get one from a breeder where you know the genetics and ancestry of the hamster (not always easy as litters aren't always frequently available).
After this bad experience as well, another option could be to look up local animal rescues and look on gumtree, and adopt a hamster that needs a home. There are many unwanted pets. And some quite young, not all older hamsters. That would be reassuring in a way. Particularly an adoption from a rescue where they would know if there was any illness and they would have cared for them well.
It sounds like you have a lot of toys and items from the large cage and nice big playpen, and these are expensive to replace and often difficult to disinfect some things. So maybe get prepared now. Something like a pet safe disinfectant is better to use than bleach in my opinion, and is what vets use. Even then rinsing and airing well is good afterwards as hamsters have a strong sense of smell and can be affected by scents.
This is the one our vet recommended
https://www.amazon.co.uk/Johnsons-Cl...r+disinfectant
Plastic toys and metal items can just be sprayed/wiped with this, rinsed and dried. I found cage bars a real pain to get to every bit - I put the cage top in the bath to spray and wipe and then filled the bath to rinse it.
Wood or natural items like stone can be baked - I can't remember the temperature or how long, but someone will know. Although personally I think rough wood bark items like bendy bridges are best replaced. For that reason i have very few bark wood items these days! After having had to do a full disinfect once.
Cardboard is your friend! cheap toys, hamsters like chewing them, and easily replaced. Cardboard tunnels, egg box hides, shoe box houses etc. Boredom breakers make some nice colourful cardboard tubes/tunnels.
Ceramic is easy too. Painting smooth wood items like houses with plastikote makes them easy to disinfect as they have a waterproof coating on that is easily sprayed and wiped. Plastic is fine too.