fix excessive calls to format-tab-title

* Removed title update from main render loop
* Add to PaneFocused event
* term: only emit Alert::OutputSinceFocusLost for the first
  seqno bump after losing focus, rather than on every bump.
  That event indirectly causes the title to update

refs: https://github.com/wez/wezterm/issues/4788

docs/changelog.md

@@ -175,6 +175,8 @@ As features stabilize some brief notes about them will accumulate here.
   accounts for window padding. Thanks to @jknockel! #4824
 * Bar shaped text cursors are now rendered above text. Thanks to
   @ErrorNoInternet! #4850
+* `format-tab-title` event was triggered excessively for background tabs/panes.
+  Thanks to @crides for investigating! #4788
 
 #### Updated
 * Bundled harfbuzz to 8.3.0

term/src/terminalstate/mod.rs

@@ -378,7 +378,10 @@ pub struct TerminalState {
 
     accumulating_title: Option<String>,
 
+    /// seqno when we last lost focus
     lost_focus_seqno: SequenceNo,
+    /// seqno when we last emitted Alert::OutputSinceFocusLost
+    lost_focus_alerted_seqno: SequenceNo,
     focused: bool,
 
     /// True if lines should be marked as bidi-enabled, and thus
@@ -575,6 +578,7 @@ impl TerminalState {
             enable_conpty_quirks: false,
             accumulating_title: None,
             lost_focus_seqno: seqno,
+            lost_focus_alerted_seqno: seqno,
             focused: true,
             bidi_enabled: None,
             bidi_hint: None,
@@ -795,8 +799,15 @@ impl TerminalState {
 
     pub(crate) fn trigger_unseen_output_notif(&mut self) {
         if self.has_unseen_output() {
-            if let Some(handler) = self.alert_handler.as_mut() {
-                handler.alert(Alert::OutputSinceFocusLost);
+            // We want to avoid over-notifying about output events,
+            // so here we gate the notification to the case where
+            // we have lost the focus more recently than the last
+            // time we notified about it
+            if self.lost_focus_seqno > self.lost_focus_alerted_seqno {
+                self.lost_focus_alerted_seqno = self.seqno;
+                if let Some(handler) = self.alert_handler.as_mut() {
+                    handler.alert(Alert::OutputSinceFocusLost);
+                }
             }
         }
     }

wezterm-gui/src/termwindow/mod.rs

@@ -1228,7 +1228,8 @@ impl TermWindow {
                     // Handled by frontend
                 }
                 MuxNotification::PaneFocused(_) => {
-                    // Handled by clientpane
+                    // Also handled by clientpane
+                    self.update_title_post_status();
                 }
                 MuxNotification::TabResized(_) => {
                     // Handled by wezterm-client

wezterm-gui/src/termwindow/render/paint.rs

@@ -114,7 +114,6 @@ impl crate::TermWindow {
         );
         metrics::histogram!("gui.paint.impl", self.last_frame_duration);
         metrics::histogram!("gui.paint.impl.rate", 1.);
-        self.update_title_post_status();
 
         // If self.has_animation is some, then the last render detected
         // image attachments with multiple frames, so we also need to