E-mail app version 126.96.36.199, latest version according to app "about" info dialogue.
Lately my IMAP accounts which I use in parallel on multiple devices (Samsung S7 phone with Android 8, 2 PCs, tablet) are not longer in sync because the Samsung app neither fetches not pushes read/unread status changes from/to the IMAP server. I double-checked with other IMAP clients, they always sync correctly.
Another problem is that e-mails deleted (i.e. moved to the trash folder) on the server via another app are kept in the inbox on the Samsung client forever, i.e. I have to delete them there a second time. If I look into the trash folder from the Samsung app, I actually see the deleted message there and after deleting the copy from the inbox I even see it twice.
I think that a recent update broke the IMAP support somehow. My typical workflow of reading messages on the phone, marking important ones in need of a reply as unread and then replying from the PC later, focusing on unread messages, just does not work anymore. It used to work for ~4 years, i.e. since I own my S7.
I too have this same issue and wish Samsung would fix it. It is also no longer syncing the moving of emails into other folders either. Similar to the delete issue you mentioned, if you move a message to another folder, it places a copy in the new folder but still leaves the original in the Inbox.
no longer syncing the moving of emails into other folders
Well, I said that already:
e-mails deleted (i.e. moved to the trash folder) on the server via another app are kept in the inbox on the Samsung client forever
So your problem is exactly as I described mine.
I am seeing the read/unread status issue in the Samsung email app (using IMAP). For me, the Samsung app does fetch the read/unread status if changed elsewhere (e.g. if I mark an email as read in Gmail, refresh Gmail then refresh email on Samsung, the Samsung app will show the email as read as expected). However, if I mark an email as read in the Samsung app, refresh email on Samsung then refresh Gmail, I won't see the updated read status in Gmail.
Interestingly, if I delete an email from the Samsung app, refresh email on Samsung and then refresh Gmail, all emails above the deleted email will now show the correct read/unread status in Gmail (and, the email deleted from Samsung is also removed from Inbox in Gmail).
Galaxy Note 9, Samsung email app version 188.8.131.52 (shown as latest version installed)