I have used K-9 Mail on a Pixel 6 with GrapheneOS for about a year. Email is synchronized with the server, and I get notifications of new email.
I bought a Pixel Tablet and installed GrapheneOS. I installed K-9 Mail and configured it with K-9 Mail's export/import feature, so it has exactly the same settings as on the phone.
I see the "@" notification on the status bar which indicates that K-9 Mail is waiting for new emails.
When I tap that notification for more information, it displays the following:
"When using Push, K-9 Mail maintains a connection to the mail server. Android requires displaying an ongoing notification while the app is active in the background." (Server push is a feature of IMAP and does not require Google services.)
"Allow background usage" is enabled for K-9 Mail in Settings>Battery Usage. The old "disable battery optimization" for an app seems to have vanished in Android 14, presumably replaced with "allow background usage".
I see no difference in how the tablet and phone are configured, yet the phone syncs email and gives a notification when new email has arrived, but the tablet does not. On the tablet, I must open the app and do a manual sync to retrieve new messages.
Is there a trick to get K-9 sync working? Some setting I've missed?