New answers tagged imap
On iCloud/Google Apps you didn’t create the folders under “Inbox”, and so they appear further down in the pane you’ve screenshotted. On the Exchange server you did create folders under the “Inbox”, and therefore that is where Mail.app displays them. On my Zoho (IMAP account), I can either use the web client to create folder under the Inbox, or use Mail.app ...
IMAP and Exchange both keep your email on the server. Adding the account on a new computer will allow you to access your existing email on a new local machine. While you didn't mention POP3 in your question, that would be the email protocol that was designed to store your messages locally. IMAP and Exchange protocols came later.
The following solved the issue for me: Gmail Settings: Inbox → Categories: Select only Primary Inbox → Importance markers: No marker Inbox → Filtered mail: Override filters Forwarding and POP/IMAP → IMAP Access: When I mark a message in IMAP as deleted: Auto-Expunge off When a message is marked as deleted and expunged from the last visible IMAP folder: ...
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