fix(qt): move the cortinilla debounce from QML into Rust

The 220ms debounce wrapped the WHOLE searchLive invokable in QML, so live()
- which opens the dropdown and raises the skeleton - only ran 220ms after
the LAST keystroke. Continuous typing therefore showed nothing at all. The
reference opens the panel and raises the skeleton on the FIRST keystroke of
2+ characters and debounces only the LOAD.

live() is now two halves. The synchronous half runs on the first poll of the
spawned task, i.e. at the keystroke: gates, selection reset, open, query,
version bump, loading flag. Then it sleeps 220ms and re-checks the version,
so a superseded task exits without touching the network. This is the shape
the immersive arm already uses (imm_live), which is the precedent in both
respects: raise synchronously, debounce the load.

cortinillaLoading gets exactly one owner in the synchronous half and is
written once more at the publish - never in both halves for the same
keystroke.

Two consequences ride along:

  - dismiss() becomes a real cancellation point. It only flipped the open
    flag, so an in-flight load survived Esc, published into a closed
    dropdown and rewrote LAST_CORT. It now bumps the version too. This
    matters more now that the version bumps per keystroke.
  - the idle-close timer restarts on the QUERY rather than the payload. A
    burst of typing publishes one payload but many queries, and the
    reference restarts per keystroke.

HeaderBar.qml's header claimed the cortinilla and live-search were "out of
scope" in the file that wires the whole input path. Corrected here, beside
the code that falsifies it, rather than in a later docs sweep.

Contract: qbz-nix-docs/qt-frontend/2026-08-03-cortinilla-parity, commit C3
(H1/H2/H3/H8, D-BUG-8, R7-4).

Gate: build clean, 256/256 tests, both QML audits OK, offscreen smoke
0 complaints + home published.

cc

crates/qbz-qt/qml/shell/Cortinilla.qml

@@ -61,8 +61,11 @@ Item {
     }
     Connections {
         target: QbzSearch
-        // Activity restarts the countdown (keystroke or arrow move).
-        function onCortinillaJsonChanged() { if (root.visible && !root.panelHovered) idleClose.restart() }
+        // Activity restarts the countdown (keystroke or arrow move). The
+        // keystroke probe is the QUERY, not the payload: the reference
+        // restarts per keystroke, and now that the debounce lives in Rust a
+        // burst of typing publishes one payload but many queries.
+        function onCortinillaQueryChanged() { if (root.visible && !root.panelHovered) idleClose.restart() }
         function onCortinillaSelectedIndexChanged() { if (root.visible && !root.panelHovered) idleClose.restart() }
         // Keyboard scroll-into-view: the controller publishes the selected
         // row's content-space top-y; nudge the Flickable so it is visible.

crates/qbz-qt/qml/shell/HeaderBar.qml

@@ -15,8 +15,12 @@
 //
 // The search field gives up 60px whenever the nav is in the header, and
 // re-centers with a 220ms animation (HeaderBar.slint:569).
-// Center: the search field, absolutely centered on the window (VISUAL
-// replica — the cortinilla/live-search is out of scope; POC-NOTE).
+// Center: the search field, absolutely centered on the window. It owns the
+// live-search input path: the >= 2-char gate and the dismiss below it, the
+// arrow/Enter/Escape rules, the ↵ affordance and clearSearch(). The 220ms
+// debounce is NOT here — it lives in Rust (search_qt::live), so the panel
+// opens on the first keystroke instead of 220ms after the last one. The
+// dropdown itself is shell/Cortinilla.qml.
 // Right: the tri-state offline status badge with its flyout (recovery
 // "Sign in" wired to QbzSession.recoveryLogin) and the app menu (user block
 // + Keyboard Shortcuts + Documentation + Log Out + Close. Still missing vs
@@ -665,24 +669,21 @@ Rectangle {
             verticalAlignment: Text.AlignVCenter
             horizontalAlignment: text === "" && !activeFocus ? Text.AlignHCenter : Text.AlignLeft
             clip: true
+            // No QML debounce: the 220ms CORTINILLA_DEBOUNCE lives in Rust
+            // now (search_qt::live). Debouncing the whole invokable here
+            // meant the panel and its skeleton only appeared 220ms after the
+            // LAST keystroke, so continuous typing showed nothing at all;
+            // the reference opens on the FIRST keystroke >= 2 chars and
+            // debounces only the LOAD. Rust's version guard is what discards
+            // the superseded loads.
             onTextEdited: {
                 if (text.trim().length < 2) {
-                    liveDebounce.stop()
                     QbzSearch.cortinillaDismiss()
                 } else {
-                    liveDebounce.restart()
+                    QbzSearch.searchLive(text)
                 }
             }
 
-            // 220ms live debounce (CORTINILLA_DEBOUNCE — one load per pause,
-            // not one per keystroke).
-            Timer {
-                id: liveDebounce
-                interval: 220
-                repeat: false
-                onTriggered: QbzSearch.searchLive(searchInput.text)
-            }
-
             // The Enter rule (HeaderBar.slint on-enter): cortinilla open +
             // a keyboard selection -> activate the row; open + none -> full
             // search; closed -> plain submit (also Search > All).