Allow customize.yaml to override state and attribute icons in the UI

[PlasmaPod]

Describe the enhancement

Add support for defining state-level and attribute-level icon overrides via customize.yaml so users can control how entities are visually represented in the Home Assistant UI.

Currently, customize.yaml only supports setting a single static icon per entity. Many entities expose multiple meaningful states or modes (for example fan modes, preset modes, actions, media states, or cover states), and the UI uses built-in icon mappings that users cannot override.

This enhancement would allow users to define optional icon mappings in customize.yaml that the frontend can use when rendering entities.

Use cases

• Custom integrations often expose unique or domain-specific states that Home Assistant cannot realistically provide predefined icons for.
• Users may want certain states or modes to use different icons than the built-in defaults.
• Avoids creating specific state attributes for every integration out there making management painful

Visual examples (Current UI)

Climate entity fan modes all use the same generic mdi:circle-medium when the state is not listed in /core/homeassistant/components/climate/icons.json

Proposed improvement:

Users can define mappings in customize.yaml to customize attribute icons that are not covered by the domain component such as:

climate.living_room:
  icon: mdi:air-conditioner

  state_icons:
    cool: mdi:snowflake
    heat: mdi:fire

  attribute_icons:
    fan_mode:
      quiet: mdi:volume-mute
      low: mdi:speedometer-slow
      medium_low: mdi:speedometer-slow
      medium: mdi:speedometer-medium
      medium_high: mdi:speedometer-high
      high: mdi:speedometer-high
      auto: mdi:fan-auto
      strong: mdi:weather-windy

The UI then displays these icons wherever the entity is shown, including in dropdown selection boxes in Image 2

Potentially Related Discussions:

#264 Allow customizing entity icon based on state
#1467 Customise or create new device_class to better represent entities states

Relevant Documentation

https://www.home-assistant.io/integrations/homeassistant/#manual-customization
https://github.com/home-assistant/core/blob/dev/homeassistant/components/climate/icons.json

Notes

This is intended as a UI override mechanism, not a request to add icons for specific integrations.
If no custom mappings are defined, the UI should continue to behave exactly as it does today.
This feature would be additive and backwards compatible.