Track iOS custom notification icon support for local alerts

## Source
- Split from #1772 item 1.
- Upstream reference: https://github.com/home-assistant/iOS/pull/4672
- Related digest context: #1771 item 1 also surfaced this same iOS notification icon idea.

## Idea
Home Assistant iOS is adding support for custom notification icons in push payloads through fields such as `notification_icon` and `icon_url`. Once the iOS app and push relay support are fully available, local alerts could show task-specific icons instead of the default Home Assistant app icon.

## Local direction
- Confirm the iOS app release and payload support before changing Home Assistant YAML.
- Update the shared notification script/package path to accept optional icon fields without changing existing notification behavior.
- Start with high-signal alerts where icons add context, such as backup status, appliance completion, cameras, and health/coaching reminders.
- Keep the implementation optional so existing Android/iOS notification flows continue to work unchanged.

## Acceptance notes
- Notification icon fields are documented in the local package/script comments or README if behavior changes.
- A small set of high-value alerts includes meaningful icons.
- Home Assistant config validation passes after any YAML changes.

Start by checking the upstream iOS reference and confirming that the app release and push relay support notification_icon and icon_url. Then inspect the shared notification script/package path and the existing high-value alerts named in the issue. Done means optional icon fields preserve current notification behavior, selected alerts use meaningful icons, behavior is documented, and Home Assistant config validation passes.

Written by the indexing model from the issue text.