/e/ apps take several hours to receive synchronization from the cloud server

I will copy my answer to this question here in case it helps someone else find it.

Is there usually something specific that you need to synchronise?
In some apps you can sync things more easily, e.g. in my calendar it is three dots and then sync all - only two gestures.
For syncing everything more often, you could try going to settings → Accounts → Your murena account name → Account extra settings → Click on your account name again → Settings gear icon top right → change your sync intervals
I have my contacts set to sync every 2 hours, but my calendars every 2 minutes for example