I do IT support and mobile devices for my company and we are starting to get complaints about these issues after upgrading to 13/13.1. 13.1 is a bit better but its still very buggy.
I have the same issue on Exchange. It can take over a minute to download email headers and, when I open a message, another more-than-a-minute to download the body. Glad to see that multiple others are having this problem. It may help Apple to take it seriously.Same issue...emails not downloading in my Exchange account. 13.1 didnt fix it as hoped. Deleted email account and set it up from scratch, emails still not downloading. I get the headers and multiple banner notifications for each message but audio notifications dont work. This has been a complete fiasco. How could Apple not have tested a basic component as their Mail app??