AsteroidOS, which runs on many Android watches, and offers a Linux environment over SSH and WiFi (for watches that support it). https://asteroidos.org/

The simplest integration is writing a daemon (in the language of your choice) that schedules wakes, syncs, and sends FreeDesktop notifications.

If you want more of a UI, then you'll be writing QtQuick, which is QML/Javascript/C++.

Their best supported watch is the TicWatch Pro: https://asteroidos.org/watches/catfish/