I don't have any reason to believe that it's Aqua Mail doing it.
I don't have any reason to believe that Aqua is setting messages as read "on its own".
How is the account set up in the app now (not before)? Please long press on the account on the app's main screen -> options and folders -> you'll see one of
IMAP Options
POP3 Options
Exchange Options
Which it is?
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Is the old phone where you have the app still "alive"? Is it turned on?
Is the account still set up there?
If so, how is that set up, IMAP / POP3 / Exchange?
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Finally, if you log into web mail (your mail provider's web site) - are your messages *read* there or still unread?
What is the mail provider? Gmail / Yahoo / Hotmail / corporate / something else?