Draw idle as one timeline, and let the power button answer to its owner

Claude-Session: https://claude.ai/code/session_01Ms2FbjQy31TVf3CEvQhGM8

config/dot/quickshell/services/SettingsSearch.qml

@@ -34,6 +34,7 @@ Singleton {
         "datetime": "datetime",
         "battery": "power",
         "idleBattery": "power",
+        "power": "power",
         "typography": "appearance",
         "themes": "appearance",
         "titlebar": "appearance",
@@ -148,6 +149,18 @@ Singleton {
         { label: "Performance overlay", detail: "Frame rate and sensors on top of the game", page: "gaming" },
         { label: "Proton", detail: "Compatibility tools available to Steam", page: "gaming" },
         { label: "Graphics card", detail: "Temperature, power draw, and video memory", page: "gaming" },
+        // Power & Lock. The sliders come from the schema, but the subjects
+        // people arrive with are the physical ones — a button, a lid, sleep —
+        // and none of those is the label of a preference. Hibernate is the
+        // sharpest case: it has no control at all, only an honest row saying
+        // why this machine will not do it, and a search that found nothing
+        // would read as the desktop having no opinion.
+        { label: "Hibernate", detail: "Whether this machine can hibernate, and why zram swap means it does not", page: "power" },
+        { label: "Power profile", detail: "Power saver, balanced, or performance, applied system-wide", page: "power" },
+        { label: "Power button", detail: "What pressing it does: the power menu, suspend, power off, or nothing", page: "power" },
+        { label: "Lid", detail: "What closing the lid does, and why an external display changes it", page: "power" },
+        { label: "Suspend", detail: "When the machine sleeps on its own, on wall power and on battery", page: "power" },
+        { label: "Sleep", detail: "The idle timeline: screen off, then lock, then suspend", page: "power" },
         { label: "Software update", detail: "Packages, applications, and firmware", page: "updates" },
         { label: "Updates", detail: "What is waiting to be installed", page: "updates" },
         { label: "Firmware", detail: "Updates for the hardware itself", page: "updates" },