They had me change a setting in Outlook to "Leave a copy of the deleted emails on the server"..I chose for 7 days.
Which implies that it wasn't enabled before. And even with the "for 7 days" -- Outlook *will* delete any messages older than 7 days.
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It's not possible, AFAIK, to change from POP3 to IMAP in Outlook or any other mail app.
Only to remove the account from Outlook (or any other mail app) and then to add back, being careful with the settings.
In AquaMail, I assume it's IMAP already, but please check: long press the account -> options and folders and you'll see either "IMAP options" or "POP3 options".
If not, you will also want to remove the account and add it back -- after entering your email + password, please press Manual and not Next, and be sure to select "IMAP" near the top of the next screen (incoming server settings), and then you may need to update the server name / encryption / port #.
I belive it's "imap.i<redacted but you should recognize it>r.com", SSL, port 993. And for the outgoing, smtp.i...r.com, SSL, port 465.