[WIP] Align all time formatting options

[Copilot]

Task: Align all time formatting options

Based on PR #22339, this task aims to complete the work to add customizable time format options for relative time display across the frontend.

Plan:

• Add format parameter support to relativeTime() function in src/common/datetime/relative_time.ts (narrow, short, long styles)
• Update TIMESTAMP_RENDERING_FORMATS to include relative_narrow and relative_short
• Add format property to ha-relative-time component
• Update hui-timestamp-display component to support new formats
• Add format property to state-display component
• Update badge and tile card configs to include format option
• Update editor structs for tile-card and entity-badge
• Update all tests to handle new optional format parameter
• Ensure all places using timestamp display components can pass format through
• Run linting and tests to ensure no regressions

Key changes from PR #22339:

• Use format as the property name (not time_verbosity)
• Support relative, relative_narrow, relative_short as format options
• Pass format through component hierarchy properly
• Keep backwards compatibility (default to relative / long style)

Original prompt

Create a task to finish the work started in #22339 and align all the time formating options

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