symon As a GNOME user who hasn’t even enabled SOGo, I can confirm that IMAP works flawlessly in GNOME.
I set up my mail accounts through GNOME Online Accounts and use Evolution as my client. Emails arrive instantly, including GNOME notifications. The same goes for CalDAV/CardDAV, which in my case run through my Nextcloud. Those also integrate perfectly with both Evolution and the standalone GNOME Calendar and Contacts apps.
In short: if you use GNOME, there is absolutely no reason to rely on re-implementations of proprietary Microsoft technologies.
The only possible reason to keep ActiveSync would be for a smartphone. But even there, in my opinion, it isn’t necessary. I use K-9 on my Android phone, and it uses a background service to listen for new messages. The battery impact is minimal (I have three accounts set up).