fix: the sidebar button follows the panel, and the wish survives having no source

The toolbar button was the panel's only input: `update_side_visibility()` derived the
panel from the button and never the other way, so the button went on saying "shown" in
two cases where the panel was off -- while there were no signals to show, and after
anything else moved the split view's state.

Binding the two together is not the fix. AdwOverlaySplitView writes `show-sidebar`
itself, at startup and when it collapses, with no user involved; a binding pushes that
into the button, the button's handler reads it as the user's wish, and the sidebar then
never comes back when a source connects -- a worse bug than the one reported, and one
that a "was this our own write" flag does not catch either, because the toggle's signal
may fire after the write returns.

So the direction is stated instead of inferred: `show-sidebar` is an output, the button
is the only input, and `App::sidebar_wanted` holds the wish between them. The wish is
written by the toggle's handler alone (guarded while we set the button ourselves), the
no-signals case forces the panel off without touching the wish, and tick() re-asserts
both from the wish when the widget disagrees -- so a hide gesture does not stick either.

[sidebar-probe] now reads the pair (shown vs button) in both states and against a hide
that did not come from the button; shown=1 button=1 with a source, shown=0 button=0
without, and the source reconnecting brings both back is the reading this exists for.

src/ui.cpp

@@ -2751,13 +2751,20 @@ void on_right_click(GtkGestureClick* gesture, int, double x, double y, gpointer
 void update_side_visibility(App& app) {
   if (app.side_scroll == nullptr) return;
   const bool have_signals = !app.model->signals().empty();
-  const bool want_column =
-      have_signals && gtk_toggle_button_get_active(GTK_TOGGLE_BUTTON(app.sidebar_toggle));
+  // `have_signals` decides whether the sidebar *can* be on; `sidebar_wanted` is the user's last word,
+  // which is why it is kept apart from the button's own state -- that state follows the panel now, and
+  // the panel is off while there is nothing to show. A swipe that hides the sidebar fires the button's
+  // handler (the binding is bidirectional), so a gesture is a choice too.
+  gtk_widget_set_sensitive(app.sidebar_toggle, have_signals);
+  const bool want_column = have_signals && app.sidebar_wanted;
   // The split view owns the sidebar's visibility: it animates it, and when the window is too narrow it
   // shows it as an overlay rather than letting the column be squeezed to nothing. Hiding the scroller
   // instead left an empty column where the panels should be.
   if (app.side_view != nullptr) {
+    app.sidebar_syncing = true;
     adw_overlay_split_view_set_show_sidebar(ADW_OVERLAY_SPLIT_VIEW(app.side_view), want_column);
+    gtk_toggle_button_set_active(GTK_TOGGLE_BUTTON(app.sidebar_toggle), want_column);
+    app.sidebar_syncing = false;
   }
   gtk_widget_set_visible(app.signal_toggle, have_signals);
   gtk_widget_set_visible(app.trigger_toggle, have_signals);
@@ -2765,10 +2772,13 @@ void update_side_visibility(App& app) {
 
 void on_sidebar_toggled(GtkToggleButton* button, gpointer user) {
   App* app = static_cast<App*>(user);
-  (void)button;
+  // Only a state we did not write is a wish: `update_side_visibility` sets this button (and the panel)
+  // from `sidebar_wanted`, so an unguarded change here is the user's.
+  if (!app->sidebar_syncing) app->sidebar_wanted = gtk_toggle_button_get_active(button) != FALSE;
   update_side_visibility(*app);
 }
 
+
 // --- rebuild of the derived panels -----------------------------------------
 
 
@@ -3627,6 +3637,18 @@ gboolean tick(gpointer user) {
   // to nothing. `kSidebarRoom` is the sidebar's 320 plus the width below which the plot stops being
   // worth looking at.
   if (app->side_view != nullptr && app->window != nullptr) {
+    // The split view writes `show-sidebar` itself (at startup and when it collapses), so the wish is
+    // re-asserted here -- but only when they disagree, so a settled frame touches nothing. This is also
+    // why a hide *gesture* does not stick: the panel is where the button says it is.
+    const bool want = !app->model->signals().empty() && app->sidebar_wanted;
+    if (adw_overlay_split_view_get_show_sidebar(ADW_OVERLAY_SPLIT_VIEW(app->side_view)) != want) {
+      adw_overlay_split_view_set_show_sidebar(ADW_OVERLAY_SPLIT_VIEW(app->side_view), want);
+      if (gtk_toggle_button_get_active(GTK_TOGGLE_BUTTON(app->sidebar_toggle)) != want) {
+        app->sidebar_syncing = true;
+        gtk_toggle_button_set_active(GTK_TOGGLE_BUTTON(app->sidebar_toggle), want);
+        app->sidebar_syncing = false;
+      }
+    }
     const int window_w = gtk_widget_get_width(app->window);
     if (window_w > 0) {
       adw_overlay_split_view_set_collapsed(ADW_OVERLAY_SPLIT_VIEW(app->side_view),
@@ -4437,6 +4459,11 @@ void on_activate(GtkApplication* application, gpointer user) {
   // this is where it went when the window moved into the file, and it is why the window came up small.
   gtk_window_set_default_size(GTK_WINDOW(app->window), 1280, 800);
 
+  // Nothing listens to the split view's own `show-sidebar`: it is an *output*. `AdwOverlaySplitView`
+  // writes it itself -- at startup, and when it collapses -- and reading that back as user input is what
+  // made connecting a source leave the sidebar shut. The button is the only input; `update_side_visibility`
+  // re-asserts the wish on top of the widget (see the tick).
+
   // The badge and the text share one row so the badge sits at the line's head. It is a
   // sibling rather than part of the label's own markup because the label's text is
   // rewritten every frame and its markup is ellipsized -- a blinking span inside it would