Support additional actions for Entity Heading Badges

[ClayBenson94]

Summary

Right now it seems as if entity heading badges only support tap_action, while regular entity badges support tap, double tap, and hold. Would it be possible to have them support those actions as well?

I have a dashboard that uses headings which contain badges for a few light entities, and while the tap_action works great, it'd be awesome if I could configure them to have a hold_action as well!

Here's an example of my current configuration, with the suggested improvement

type: heading
icon: mdi:sofa
heading: Living Room
heading_style: title
badges:
  - type: entity
    show_state: false
    show_icon: true
    entity: light.hallway_light
    color: state
    tap_action:
      action: toggle
    hold_action: # This is what I would like to be able to do!
      action: more-info

Investigations

I've contributed a bit to home-assistant/core before, but never to the frontend, so I unfortunately don't have a great understanding of the complexity of a change like this, but I did do some digging to try and identify what might need to change to support something like this, so I'd love a gut-check if there's anything else I'm missing!

From what I can tell, the hui-entity-badge component already supports this (along with hasDoubleClick), so it just seems like the hui-entity-heading-badge doesn't -- perhaps some of the approach used in the former component could be ported to the latter?

frontend/src/panels/lovelace/badges/hui-entity-badge.ts

Lines 207 to 218 in ef7f499

	<ha-badge
	.type=${this.hasAction ? "button" : "badge"}
	@action=${this._handleAction}
	.actionHandler=${actionHandler({
	hasHold: hasAction(this._config!.hold_action),
	hasDoubleClick: hasAction(this._config!.double_tap_action),
	})}
	.label=${label}
	.iconOnly=${!content}
	style=${styleMap(style)}
	class=${classMap({ active })}
	>

[ClayBenson94]

I created #24707 to attempt to address this. It's still kind of a work in progress, but sharing for visibility!