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-tray/src/status.rs

@@ -75,7 +75,7 @@ impl TrayStatus {
             TrayStatus::Degraded => "punktfunk host — running (status unavailable)".into(),
             TrayStatus::Error(e) => format!("punktfunk host — failed ({e})"),
             TrayStatus::Running(s) => {
-                let base = match (&s.session, s.video_streaming) {
+                let base = match (&s.session, self.is_streaming()) {
                     (Some(sess), true) => format!(
                         "punktfunk host {} — streaming {}×{}@{}",
                         s.version, sess.width, sess.height, sess.fps
@@ -113,8 +113,23 @@ impl TrayStatus {
         matches!(self, TrayStatus::Running(s) if !s.conflicts.is_empty())
     }
 
+    /// A client is streaming: the host's flag, OR a live session in the summary.
+    ///
+    /// The session is checked too because a host from before the `get_local_summary` fix raised
+    /// `video_streaming` from the GameStream plane only — through a whole session on the native
+    /// (default) plane it said false while still reporting that session's mode, which is what left
+    /// the tray sitting at "idle" mid-stream. This keeps a newer tray honest against such a host.
     pub fn is_streaming(&self) -> bool {
-        matches!(self, TrayStatus::Running(s) if s.video_streaming)
+        matches!(self, TrayStatus::Running(s) if s.video_streaming || s.session.is_some())
+    }
+
+    /// Virtual displays held with no live session (lingering/pinned) — offered as a one-click
+    /// release in the menu, since holding one can also be keeping physical monitors dark.
+    pub fn kept_displays(&self) -> u32 {
+        match self {
+            TrayStatus::Running(s) => s.kept_displays,
+            _ => 0,
+        }
     }
 
     /// A pairing attempt is waiting on the operator (shown as an extra menu entry).
@@ -156,9 +171,11 @@ struct Shared {
 
 impl Poller {
     /// Spawn the poll thread; `on_change(status, console_up)` fires (from that thread) whenever
-    /// either changes. `console_up` is a live loopback probe of the web console on `web_port` —
-    /// ground truth for the "Open web console" menu entry (a layout sniff would miss consoles run
-    /// from a repo checkout, and shows a dead entry while an installed console is still starting).
+    /// either changes. `console_up` is a live loopback probe of the web console on `web_port`. It
+    /// annotates the "Open web console" entry ("not responding") rather than hiding it: the entry
+    /// is the tray's most-wanted action, and a menu that silently drops it — because the console
+    /// was still starting, or the probe timed out — is indistinguishable from a tray that never
+    /// had one.
     pub fn spawn(
         mgmt_addr: String,
         mgmt_port: u16,
@@ -203,6 +220,10 @@ fn poll_loop(
     // When the summary became unreachable while the service was running (grace anchor).
     // Runs for the process lifetime (the tray exits by process exit; nothing to unwind).
     let mut unreachable_since: Option<Instant> = None;
+    // Consecutive failed console probes. One miss is not "down": the console is a bun/Nitro SSR
+    // whose cold first render can outrun this agent's 2 s timeout, and a menu entry that changes
+    // its label every few seconds reads as broken.
+    let mut console_misses = 0u32;
     loop {
         let svc = probe_service();
         let summary = if svc == ServiceState::Running {
@@ -219,7 +240,13 @@ fn poll_loop(
         };
         let grace_expired = unreachable_since.is_some_and(|t| t.elapsed() >= START_GRACE);
         let status = map_status(&svc, summary, grace_expired);
-        let console_up = probe_console(&agent, &console_url);
+        let console_up = if probe_console(&agent, &console_url) {
+            console_misses = 0;
+            true
+        } else {
+            console_misses += 1;
+            console_misses < 2
+        };
         if last.as_ref() != Some(&(status.clone(), console_up)) {
             on_change(status.clone(), console_up);
             last = Some((status, console_up));
@@ -478,6 +505,32 @@ mod tests {
             .contains("status unavailable"));
     }
 
+    /// A live session means streaming even if the host's flag says otherwise — a host from before
+    /// the `get_local_summary` fix only raised `video_streaming` for the GameStream plane, so a
+    /// native session showed as "idle" with its own mode printed next to it.
+    #[test]
+    fn a_live_session_reads_as_streaming_without_the_flag() {
+        let mut s = summary(true);
+        s.video_streaming = false; // pre-fix host, native session
+        let st = TrayStatus::Running(s);
+        assert!(st.is_streaming());
+        assert_eq!(
+            st.headline(),
+            "punktfunk host 0.5.1 — streaming 2560×1440@120"
+        );
+        // No session and no flag is still idle.
+        assert!(!TrayStatus::Running(summary(false)).is_streaming());
+    }
+
+    #[test]
+    fn kept_displays_are_reported_for_the_release_action() {
+        assert_eq!(TrayStatus::Running(summary(false)).kept_displays(), 0);
+        let mut s = summary(false);
+        s.kept_displays = 2;
+        assert_eq!(TrayStatus::Running(s).kept_displays(), 2);
+        assert_eq!(TrayStatus::Degraded.kept_displays(), 0);
+    }
+
     #[test]
     fn pairing_attention_flags() {
         let mut s = summary(false);