Propagate Home Assistant schedule to ESPHome devices

The ability to propagate a Home Assistant schedule to ESPHome devices.

Although it already would be possible to e.g. change the state of a switch, light etc. depending on the current state (on/off) of a Home Assistant schedule, it would be a nice feature if the schedule could get propagated from Home Assistant to the ESP whenever the schedule changes.

By having ESPHome getting the next event transferred from Home Assistant, operations would be fail-safe if for example the connection between Home Assistant and the device fails for whatever reason - such as Wi-Fi disruption.

Example:
Let's say that a ESPHome unit is controlling a pump, where it is important that the pump only operates between 8.00-9.00, 12.00-13.00 and 20.00-21.00 but times and days may be subject to occasional changes. It is easy to maintain this schedule within Home Assistant, and since it is crucial that the pump doesn't fail to start and actually does stop at indicated time, the local ESPHome schedule (or next upcoming event) is known by and handled locally in the ESPHome unit - thus making sure that a broken connection with Home Assistant won't result in the pump not starting or stopping when supposed to.

The request concerns propagating a Home Assistant schedule to ESPHome devices, including the next event or local schedule. Start by determining the integration boundary and how schedule changes reach the device; done means the device can keep the pump schedule operating through a connection failure and apply later schedule changes.

Written by the indexing model from the issue text.