iOS13 update mail app issue on iphoneX

Have had a similar issue with iOS 13 on a XS. Syncing Mail problematic, with both downloading header info into folders and rendering body text when opening individual emails.

I removed the email account entirely, and put it back on, and only syncing 1 month’s worth at the moment, and seems better. However, notification badge not showing on new mail until I open Mail app.

When you experience an issue or something does not work as expected on beta, send your feedback directly to Apple with Feedback Assistant.

Ok. Good that your have downloaded iOS 13 already. I am still doing it and will get back to you in an hour with my feedback.

Perhaps try deleting the Mail app and reloading it?