Mister catch-up exists in firmware and the brain but has no UI at all — it would run invisibly once a mister target is set

FOUND 2026-09-10 while investigating the light catch-up ask — the same debt/catch-up pattern, one layer less visible. The hub computes a mister debt exactly like the light one: tgt = mister_target_h * 3600, debt = tgt – mister_delivered_s, mister_catchup_active = debt > 0 && clone_hum_auto_enabled. The brain maps binary_sensor.dsc_hub_mister_catchup_active (hub_controls.py:409) and it is present in /fleet/computed hass_extras. But grepping frontend/src for mister_catchup returns NOTHING. The light version at least gets a CATCH-UP ACTIVE tag on the Light desk; the mister version has no badge, no explanation, no cancel, and no stated end — it is entirely invisible to the operator. Currently dormant and therefore low severity: live values are mister_catchup_active = off and number.dsc_hub_mister_target_hours = 0.0, and the mister seat is out of service (F-002). But it runs the moment a target is set, and nothing on screen would say so. FIX: surface it wherever the mister lives (Climate equipment tile), with the same three things the light catch-up now gets — what it is doing, when it is expected to end, and how to cancel it. The projection helper is generic: frontend/src/lib/lightCatchup.ts projectCatchup() takes debt/dark-remaining/floor and is not light-specific.