Hi @Tom,
My question is, if I switch to an IMAP server, will Outlook automatically export all of my PST data into the IMAP server so that I can access them, along with sent emails, using a smartphone or other devices?
The PST data needs to be imported manually and then yes, you would be able to access them across different devices.
POP3 works by contacting your email service and downloading all of your new messages from it. Once downloaded, they are deleted from the email service. IMAP works by reading data from the email service, so you would need to import the local PST file back to your mailbox so that they can be accessed when your account is configured using IMAP.
Regarding your concern about Sent Items, by default, the checkbox of "Do not save copies of sent items" is not selected when an IMAP account is added, which means sent items can be accessed on other devices as well. So, you can rest assured about it.
Below are two official documents for reference. One is about import PST files in Outlook, the other is about the difference between IMAP and POP3:
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