Sync issues / missing auto-start permission
In most cases when anything does not work correctly on a Xiaomi device, the AUTO-START permission (non-standard extension by Xiaomi) is not set for aCalendar and thus blocks various actions like notifications or tasks sync.
The auto-start permission can be set in Android/Xiaomi settings under Security - Permissions.
For widgets not responding with 3rd party launchers please activate the following setting:
Android Settings - Apps - Manage apps - aCalendar - Other permissions - Display pop-up windows while running in the background
(see here for more details about this Xiaomi bug https://forum.xda-developers.com/poco-f1/help/nova-launcher-widgets-clickable-t3841380)