MyPhoneExplorer will not backup or sync Apps and their data in one go.
You can backup or sync the whole Internal Storage, which includes the App data.
And then MyPhoneExplorer can extract the App APKs for you, one App at a time (you have to click every single App, no batch-processing), and it can install the Apps again with those APKs, one App at a time.
I wouldn’t recommend this conceptually between different Android versions and phones, though.
Better use MyPhoneExplorer to only sync contacts, calendar, pictures, notes and messages to the new phone.
Then install Apps directly on the new phone and let them arrange their data themselves. Perhaps look into the Apps’ own backup procedures, some Apps have them.