I have a similar problem. Everything was going fine until I updated IOS 13. After that everything went to ****. I have had a plethora of problems with IOS 13. Between my cursor which is now possessed and won't go anywhere that I tap, and Mail that is similarly cursed, I'm about to lose my mind.
What I'm experiencing in Mail is that is it not synchronizing correctly with my Hotmail (outlook.com) email application. I have "boomeranging" emails in my junk folder; meaning when I delete them, a number of them will return to the junk folder days or weeks later. It's very random in that a few deleted junk emails will suddenly reappear in my junk folder, but only on the iPhone. The junk folder is empty on all my other devices.
I have another synchronization problem when moving emails from one folder to another using the iPhone. For example, if I move 200 emails from one folder to another, the iPhone will move them correctly, but then it will show 75 "ghost" emails in the original folder that they were moved from. The 75 ghost emails are also properly located in the folder that I moved them to, they just also appear in the folder that I moved them from, so they are in two places at once according to the iPhone.
The ghost emails will not go away. They will sit there for weeks on end in the original folder until I decide that I can't take it anymore and I select them all and delete them. Once I do that the folder remains empty, and the original 75 emails remain in their proper place in the other folder.
The problem is clearly with IOS 13, because I never had this problem before I updated to IOS 13, and my email application synchronizes perfectly in Mail on all my other devices (iMac desktop computer and MacBook). I also have the Outlook.com app on my iPhone which synchronizes 100% properly. My email works correctly everywhere, except on my iPhone’s Mail app.
I reported these issues to Apple a number of times and have done every update since then but the problem still persists. When it first started happening I deleted my email account from the phone's Mail app and added it back in. It worked fine for a little while until the boomeranging emails started all over again. It's never the same emails that boomerang back to the junk folder. It could be half a dozen junk emails that reappear from the last couple of days or it could be 30 junk emails from the last 30 days. It's totally random.
The next thing I tried was to delete the Mail app altogether from the phone and add it back from the App store. After doing that I added my email account to the new Mail app, but unfortunately that made no difference. The exact same problems with synchronization occurred again over time. Before doing the last update to 13.3.1, I deleted my email account from the Mail app, and tethered my phone to my desktop computer and did the update that way, just in case there was a Wi-Fi glitch that was causing hiccups with the prior updates. After that I added my email account back to the Mail app, but it didn't help. The same problems reoccurred.
Unfortunately, Apple will not escalate my support ticket to the engineering department unless I first agree to restore my phone from a current backup and start over. Admittedly they said it's going to take me several days to get my phone back to the way it was after I do a restore. I said why should I have to do that when the problem is with iOS 13? I am tired of having to go through repeated time-consuming diagnostics on my own and with Apple senior support only to end up being told that there's nothing they can do to escalate the ticket unless I first agree to blow up my phone and start over. No thanks! I will wait till iOS 14 comes out and hope that these problems are resolved.
It's clear from the number of reports in the Apple support community that I am not alone in my horrific experiences with IOS 13. And don't even get me started with my possessed cursor. Chasing it around endlessly like my iPhone is a pinball game is the least of my problems.