Apple Mail message and badge sync is too slow. Is there a fix?

I just started using iCloud Mail and it's been a painful experience.

All my rules are set on iCloud server side and they work fine if I have iCloud open in the browser. But the MacOS Mail App and ios Mail client take ages to update, receive message, move messages based on icloud rules, and worst of all, if I open mail on the browser or MacOS, the ios badges and notifications will sit there for a whole minute before they're synced and disappear.

A few things to note:

• I am using an @icloud.com address with the Apple Mail apps. No other accounts connected.
• I have enabled the "push" notification type from settings already.
• This is a brand new icloud mail account. very few emails
• Devices are always close by
• I have an extremely fast wifi connection
• No issues with other email clients (e.g. Gmail's app using my gmail account)

Am I missing something? Is there a fix to this or should I just move on to a more reliable service?