Not much you can do on your housing situation, of course.
I'd just do as much as you can to keep it separate and treat the area and surfaces between them thoroughly with a mite preventative (i.e. Provent A Mite) and both enclosures according to instructions on the package. If they are present, they can easily have spread already.
Not sure there's much you can do about airborne ones in such tight spaces except hope or possibly bring the newcomer to a vet and see if they can send bloodwork for a test of the more common types and just rule them out that way. Pretty sure I've seen a way to test for IBD mentioned before and there are probably others. If it comes back negative, you'd be in the clear for that one at least.
For the future newcomer, you may be able to request sending those same tests off before you get that one and eliminate those diseases before it comes home and focus more on possible mites. You'll need to explain carefully so as not to offend, but not having a way to QT thoroughly should be enough if it is done at your expense.
Or if you can find a friend/family member who can keep an eye in the husbandry parameters & you drop by to feed/water for the QT period in a separate house (and away from any reptiles they may have), there isn't much else that would help you here that I can think of.
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