Privacy

A priori, the Apple Mail app is not sending data about your emails back to Apple. Your downloaded emails are just stored on your phone and not on Apple servers. There are some things to be aware of though:

If you have "Protect Mail Activity" enabled, then any remote content loaded from your emails (eg. images) are fetched through Apple servers. This is to protect your IP address from those remote servers. Apple claims that they do not learn anything about the remote content or your interaction with the email since the content is loaded through two proxy servers which hide the source and destination from any one server. If you still don't trust Apple to load the remote content in your emails for you then you should disable this feature, and your phone will load the images in your emails directly (revealing your IP to the sender of the email). You can disable loading of remote content completely in the same menu by turning on the "Block All Remote Content" option, and now you won't load any images linked from emails at all.

Next, if you have iCloud backup enabled then your phone backup will be stored in iCloud, and this will contain all of the email data stored on your phone. By default iCloud backups are not end-to-end encrypted, so if the Apple cloud was breached, or if your account is breached, then those backups could reveal all data stored on your phone. To mitigate this, you should enable Advanced Data protection, which then enables end-to-end encryption for the other pieces of data stored in iCloud, including your backups.

Edit: please reply instead of downvoting. If there is something wrong or misleading in this comment then it benefits everyone to know what that is.