Add ability for ESP Home device using API maintain state in HA

**Describe the problem you have/What new integration you would like**

I have devices using API that sleep and only report in periodically. When HA is restarted the state of those devices goes to unknown until the next time they report in. I would like two changes:
1. HA remembers the current state of ESP Home devices using API across restarts and only changes values if the device reports changes or the device doesn't report in for a user-selected timeout.
2. Add a sensor parameter to set a timeout from the last report in for a device to go to the unknown state.

**Please describe your use case for this integration and alternatives you've tried:**

**Additional context**

No repository files, tests, or entry points are named. Start by locating the ESPHome API integration and the Home Assistant state-restoration path, then clarify how persisted state and a configurable last-report timeout should interact. Done means sleeping devices retain state across restarts and become unknown after the selected timeout.

Written by the indexing model from the issue text.