Unfortunately, Apple does not provide a direct method for extracting or viewing detailed email logs (like delete actions, moving messages between folders etc.) on an iPhone. This information is generally not made accessible to users for privacy and security reasons.
Only basic logs (like fetch logs or error logs) can be obtained, and they don’t include the type of detailed activity you’re seeking. For these logs, you can use Apple’s Console app on a Mac to view them if the iPhone is connected to the Mac, but it requires certain technical skills to filter and interpret the data.
If you suspect unauthorized access or other suspicious activity, it’s recommended to change your email password and enable two-factor authentication if you haven’t already done so.
For any more detailed analysis or investigation, you might need to contact Apple Support or a cybersecurity professional.