@PleasedToBeAFlower Separation anxiety treatment is what I do (and ideally, avoidance of..)
Factor in it will take around 6 months to a year for a rescue dog to settle in.
Any separation anxiety issues - and it is normal for dogs to not want to be alone, not cope well alone, have to learn this - could also take that sort of time frame to fix.
So you need to find full cover initially, work on ensuring either any issue is fixed or that there is no issue in the first place... at the dogs pace, not the pace that suits you or your pocket... before you can bank on leaving the dog several hours between dog walker visits and people returning home.
Even dogs who have had no prior SRP's (Separation Related Problems) may well exhibit them on moving into a new home - again, this is normal and should be expected.
Preventing SRP means firstly, not leaving the dog alone at all.
Then it means working to desensitize the dog to the various visual cues and routines you will have around leaving the house.
It means building up the time they are left, sometimes in increments of a few seconds (not the 'five minutes, then ten minutes, then 15 minutes' you will so often hear suggested around the internet and even on some doggy tv shows).
If your new dog can't cope alone, then each time they are left you undo the work you put in - this means you may have to seriously re-jig how the household works. It means things like, you might prefer a dog that sleeps downstairs alone but you've got a dog who needs to sleep with a person for at least the next 6 months; arranging for everyone to be out whilst you (it will be you!) spend half an hour shuffling in and out of the front door boring your dog shitless; you spend 40 minutes parked at the end of the road watching a pet-cam, three times a week, having chucked everyone else out so you can do this in the correct context.
It is do-able, and you may get lucky and find you do not need to put in that level of work, however there is no way to tell which dog needs this level of work, until they are in your home, and you're already attached (or your kid)....
Rescues can tell you the dog has displayed no signs of SRP, a foster can tell you this too, but the reality is, dogs behaviour is relevant to their environment as well as prior learned experiences, genetics, pain levels.... so there are no guarantees.