HA mobile: progressive disclosure + clustering + global show/hide by pane size

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Audit gap (epic #52). Mobile draws the full badge at all sizes; no icon-only->icon+state->full-chip disclosure, no clustering, no global toggle. Add pane-size-driven progressive disclosure on Android + iOS. Part of the HA management overhaul epic.

[badbread]

Deferred from the active HA management overhaul (#445): rendering polish (progressive disclosure), not management completeness. Revisit after Tiers 1-2.

[badbread]

Deferred (backlog). Mobile rendering polish (progressive disclosure / clustering by pane size). Low priority; revisit if badge density becomes a real usability problem on small tiles.