Add Time Entity Support to MQTT Discovery

[palinf]

Describe your core improvement

Add Time entity support to MQTT discovery.

Currently, MQTT discovery supports many entity types (number, select, button, sensor, switch, etc.) but does not support the time entity platform, even though time entities are a core building block integration in Home Assistant (introduced in 2022.12).

This prevents MQTT devices and AppDaemon apps from creating time entities programmatically through MQTT discovery, forcing developers to use workarounds like number entities with minute conversions, text entities with manual validation, or requiring users to manually create time helpers.

Current limitations

The MQTT integration does not support time entities in discovery, which means:

1. MQTT devices cannot expose time configuration options (e.g., scheduled actions, timers)
2. AppDaemon apps using MQTT entity factory cannot create time entities
3. Developers must use suboptimal workarounds:
   • Number entities with minutes-from-midnight conversion (not user-friendly)
   • Text entities requiring manual format validation (loses time-specific UI)
   • Read-only sensors requiring external scripts to modify values
   • Manual helper creation (breaks the discovery pattern)

The MQTT discovery documentation lists supported components, and time is notably absent despite being a standard entity type.

Technical benefits

1. Consistency: Aligns MQTT discovery with other supported entity types and Home Assistant's core entity model
2. Developer experience: Allows MQTT devices and apps to expose time inputs without workarounds
3. User experience: Users get proper time pickers in UI instead of number sliders or text inputs
4. Device integration: MQTT devices can expose scheduling features (return-to-normal times, timers, etc.) cleanly
5. Completeness: Following the same discovery pattern as number, select, and other input entity types

Additional context

Related entity types that could also benefit from MQTT discovery support:

• date entities (for date inputs)
• datetime entities (for combined date+time inputs)

These would complement the existing number, select, text, and button entities already supported.

Use case example: A thermostat scheduler app that needs users to set "return to normal mode at HH:MM" - currently has no clean way to create this time input via MQTT discovery.

Home Assistant time entity documentation: https://www.home-assistant.io/integrations/time/