feat(tray): surface kept virtual displays in the tray tooltip

Stage 8 polish. `GET /api/v1/local/summary` (the tray's loopback-only unauthenticated status
source) gains `kept_displays` — the count of lingering/pinned virtual displays (held with no live
session), over the already-validated `registry::snapshot()`. The tray shows it in the idle tooltip
("idle · 1 display kept"), so a user knows a display — and, under exclusive topology, their physical
monitors — is being held (e.g. a gaming-rig `forever` pin). Release stays via the console: a
state-changing release can't be an unauthenticated endpoint, and the non-elevated Windows tray
can't read the SYSTEM-DACL'd mgmt token, so a tray release button isn't cleanly cross-platform.
`#[serde(default)]` on the tray side keeps it compatible with an older host. Tray tests green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

api/openapi.json

@@ -2671,13 +2671,20 @@
           "paired_clients",
           "native_paired_clients",
           "pin_pending",
-          "pending_approvals"
+          "pending_approvals",
+          "kept_displays"
         ],
         "properties": {
           "audio_streaming": {
             "type": "boolean",
             "description": "True while the audio stream thread is running."
           },
+          "kept_displays": {
+            "type": "integer",
+            "format": "int32",
+            "description": "Virtual displays being KEPT with no live session — lingering (keep-alive window) or pinned\n(`keep_alive: forever`). Non-zero means a display (and, exclusive, your physical monitors) is\nheld; the tray surfaces it + a one-click release. Active (in-use) displays are not counted.",
+            "minimum": 0
+          },
           "native_paired_clients": {
             "type": "integer",
             "format": "int32",

crates/punktfunk-host/src/mgmt.rs

@@ -382,6 +382,10 @@ struct LocalSummary {
     pin_pending: bool,
     /// Native pairing knocks awaiting the operator's approval (count only).
     pending_approvals: u32,
+    /// Virtual displays being KEPT with no live session — lingering (keep-alive window) or pinned
+    /// (`keep_alive: forever`). Non-zero means a display (and, exclusive, your physical monitors) is
+    /// held; the tray surfaces it + a one-click release. Active (in-use) displays are not counted.
+    kept_displays: u32,
 }
 
 /// A paired (certificate-pinned) Moonlight client.
@@ -1330,6 +1334,11 @@ async fn get_local_summary(State(st): State<Arc<MgmtState>>) -> Json<LocalSummar
         native_paired_clients,
         pin_pending: st.app.pairing.pin.awaiting_pin(),
         pending_approvals,
+        kept_displays: crate::vdisplay::registry::snapshot()
+            .displays
+            .iter()
+            .filter(|d| d.state == "lingering" || d.state == "pinned")
+            .count() as u32,
     })
 }
 

crates/punktfunk-tray/src/status.rs

@@ -33,6 +33,10 @@ pub struct Summary {
     pub native_paired_clients: u32,
     pub pin_pending: bool,
     pub pending_approvals: u32,
+    /// Virtual displays kept with no live session (lingering/pinned). `#[serde(default)]` so an older
+    /// host that doesn't send it deserializes as 0.
+    #[serde(default)]
+    pub kept_displays: u32,
 }
 
 #[derive(Clone, Copy, Debug, PartialEq, serde::Deserialize)]
@@ -71,6 +75,14 @@ impl TrayStatus {
                     s.version, sess.width, sess.height, sess.fps
                 ),
                 (_, true) => format!("punktfunk host {} — streaming", s.version),
+                // Idle, but surface a kept (lingering/pinned) display: it — and, under an exclusive
+                // topology, your physical monitors — is being held. Release it from the console.
+                _ if s.kept_displays > 0 => format!(
+                    "punktfunk host {} — idle · {} display{} kept",
+                    s.version,
+                    s.kept_displays,
+                    if s.kept_displays == 1 { "" } else { "s" }
+                ),
                 _ => format!("punktfunk host {} — idle", s.version),
             },
         }
@@ -432,6 +444,7 @@ mod tests {
             native_paired_clients: 2,
             pin_pending: false,
             pending_approvals: 0,
+            kept_displays: 0,
         }
     }