fix(tray): count native sessions as streaming, and stop hiding "Open web console"

The tray sat at "Idle" through an entire stream, and its Windows context menu
could come up without its main action. Two separate causes.

`GET /api/v1/local/summary` reported `video_streaming`/`audio_streaming` straight
from `AppState.streaming` — flags only the GameStream media pipeline raises. The
native punktfunk/1 plane is the DEFAULT (GameStream is opt-in) and never touches
them, so every native session read as idle: idle icon, and a tooltip that printed
that session's own resolution next to the word "idle" (the `session` field was
already native-aware). This is the blind spot `/status` was fixed for — see the
`session_status` module doc — which the summary kept. Both flags now OR in a live
native session, and the tray additionally treats a reported session as streaming,
so a new tray reads an older host correctly too.

The menu built "Open web console" (and the pairing entry) only while a live
loopback probe of the console had just succeeded. A console still starting, or an
SSR render slower than the 2 s probe timeout, therefore deleted the tray's
most-wanted action outright — indistinguishable from a tray that never had one,
with left-clicking the icon as the only, undiscoverable, way in. The entry is now
always present and the default item; a failed probe changes its label to
"(not responding)" instead of hiding it, and takes two consecutive misses to say
so, since one timeout is not "down".

While here: a "Release kept display…" entry when displays are held (the summary
field's own doc promised a one-click release that did not exist), and entries
deep-link to /pairing and /displays instead of all landing on the dashboard. The
Linux SNI menu mirrors all of it.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

crates/punktfunk-host/src/mgmt/host.rs

@@ -150,11 +150,13 @@ pub(crate) struct StreamInfo {
 pub(crate) struct LocalSummary {
     /// Host version (mirrors `/health`).
     version: String,
-    /// True while the video stream thread is running.
+    /// True while video is streaming on EITHER plane: the GameStream media pipeline, or a live
+    /// native (punktfunk/1) session — the default plane, invisible in the GameStream flag alone.
     video_streaming: bool,
-    /// True while the audio stream thread is running.
+    /// True while audio is streaming on either plane (same rule as `video_streaming`).
     audio_streaming: bool,
-    /// The active launch session (set by Moonlight's `/launch`, cleared on cancel/stop).
+    /// The active session: GameStream's launch (Moonlight `/launch`) when present, else the first
+    /// live native session. `null` when nothing is streaming.
     session: Option<SessionInfo>,
     /// Number of pinned (paired) GameStream client certificates.
     paired_clients: u32,
@@ -391,26 +393,27 @@ pub(crate) async fn get_status(State(st): State<Arc<MgmtState>>) -> Json<Runtime
     )
 )]
 pub(crate) async fn get_local_summary(State(st): State<Arc<MgmtState>>) -> Json<LocalSummary> {
+    // Native punktfunk/1 plane (the DEFAULT plane; GameStream is opt-in) — read ONCE and used for
+    // both the session card and the streaming flags below.
+    let native = crate::session_status::snapshot();
     // GameStream launch, else the first live native session — so the tray reflects a native session
     // too (same GameStream-only blind spot the Dashboard `/status` had; see `session_status`).
     let session = st
         .app
         .launch
         .lock()
-        .unwrap()
+        .unwrap_or_else(|e| e.into_inner())
         .map(|l| SessionInfo {
             width: l.width,
             height: l.height,
             fps: l.fps,
         })
         .or_else(|| {
-            crate::session_status::snapshot()
-                .first()
-                .map(|s| SessionInfo {
-                    width: s.width,
-                    height: s.height,
-                    fps: s.fps,
-                })
+            native.first().map(|s| SessionInfo {
+                width: s.width,
+                height: s.height,
+                fps: s.fps,
+            })
         });
     let (native_paired_clients, pending_approvals) = st
         .native
@@ -419,8 +422,10 @@ pub(crate) async fn get_local_summary(State(st): State<Arc<MgmtState>>) -> Json<
         .unwrap_or((0, 0));
     Json(LocalSummary {
         version: env!("PUNKTFUNK_VERSION").into(),
-        video_streaming: st.app.streaming.load(Ordering::SeqCst),
-        audio_streaming: st.app.audio_streaming.load(Ordering::SeqCst),
+        // Either plane counts, like `/status`: reading only the GameStream flags made the tray say
+        // "idle" (and wear the idle icon) through an entire native session.
+        video_streaming: st.app.streaming.load(Ordering::SeqCst) || !native.is_empty(),
+        audio_streaming: st.app.audio_streaming.load(Ordering::SeqCst) || !native.is_empty(),
         session,
         paired_clients: st
             .app