There are different types of mites. Demodex mites are present on all hamsters but occasionally the population grows into an infestation and causes itching etc. This usually happens to elderly or ill hamsters. These mites are invisible to the naked eye and don't affect humans or other pets.
Because demodex mites are always present on hamsters anyway, you don't generally need to clean the cage fully because you don't need to eradicate them, only get their population down to a manageable level. Sometimes this might involve regular spot on treatment for the rest of a hamster's life.
Then there other types of mites, for example tropical rat mites, which hamsters don't normally carry but can be infested by. These mites are often visible to the naked eye. They can affect any hamster and are likely to bite humans too. If you feel little bumps or see spots of blood on your hamster, it's more likely they have one of these types of mites rather than demodex. If you have an infestation of any type of visible mite you do need to clean the cage completely. For maximum effect, I recommend following these steps:
DAY 1: Treat the hamster with a spot on anti-parasitic (ivermectin or selamectin) and move them a temporary cage with a shallow layer of bedding and only non-porous accessories (e.g ceramic, painted wood, glass, plastic).
Empty the cage, throw away all the bedding. Wash the non-porous things in hot, soapy water and you can use these again right away. Anything porous like untreated wood, and especially anything with nooks and gaps like cork logs should have boiling water poured over it and then be left either outside, or in a sealed plastic bag once dry. Ideally do this all outside to avoid spreading mites in your house.
Vacuum the room where your hamster lives very thoroughly and then change the vacuum cleaner bag. Otherwise the mites will escape the bag and re-infest the room.
DAY 2: Change the bedding in the temporary cage, as live mites will have jumped off your hamster onto the bedding. It shouldn't be necessary to change the bedding again after this, unless you see a live mite.
DAY 5: Get the porous things which you left outside or in a plastic bag and pour boiling water over them again. This is case there were any eggs on them which should have hatched by now.
DAY 8: Treat your hamster again with the spot on treatment, unless your vet has recommended a different treatment schedule. The treatment kills adult mites but not eggs, so you need to treat more than once to allow eggs to hatch in between.
If there are no signs of mites on your hamster or in their bedding, at this point you can move them back into their usual cage with new bedding.
DAY 15: As above, treat your hamster again, unless your vet has recommended a different treatment schedule. So in total there are 3 treatments, spaced a week apart.
My gerbils had mites last year, and I was able to eradicate them by following the above steps (fortunately they didn't spread to my hamster). However personally I would only do this if I had actually seen visible mites, because it's very drastic and disruptive for a hamster. If you haven't seen any mites, it's much more likely to be demodex mites or some other cause. It's worth giving the anti-parasitic to see if it does have any effect. But if not, I'd consider the possibility of a bedding allergy.
As far as I know, with Cushings the baldness is typically symmetrical and it is baldness rather than just fur thinning. But there are various other hormonal causes of thinning fur.