iCloud Mail not syncing across devices

I recently moved from Gmail over to iCloud Mail as I use iCloud for everything else so thought I might as well. I am having an issue with the iOS Mail App not syncing properly between my iPhone and iPad.

When I get an email, the notification appears on both devices. But then when I go in on one device and read/archive/delete the notification remains on the other device, as if Mail isn’t syncing in the background. It stays like this until I open the Mail app and let it refresh.

The changes I make are reflected on icloud.com, I have tried restarting both devices, signing out and back into iCloud on both and made 100% sure that Push is turned on (and it clearly works because I do receive the email immediately). I am out of ideas for what to do now, can anyone help?