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.

docs/claude/invariants-plot-and-layout.md

@@ -16,6 +16,17 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   from the window's width in `tick()`) to *overlay* the plot when there is no room beside it rather than
   being squeezed. `[sidebar-probe]` reads both states: `window=756 sidebar=320` under a 2x scale is exactly
   the case that used to be zero.
+- **The sidebar's button is the only input; `AdwOverlaySplitView:show-sidebar` is an output.** The split
+  view writes that property *itself* — at startup, and when it collapses — with no user involved, so reading
+  it back as the user's wish is wrong: doing that made connecting a source leave the sidebar shut, because
+  the widget's own `false` was recorded as the user asking for it. A `GBinding` from the property to the
+  toggle is the same mistake in one line, and it cannot be told from a real change by a "is this our own
+  write" flag either, since the toggle's signal may fire after the write returns. Instead `App::sidebar_wanted`
+  holds the wish (written only by `on_sidebar_toggled`, guarded by `App::sidebar_syncing` around our own
+  `set_active`), `update_side_visibility()` is the single place that turns that wish plus "are there signals"
+  into the panel's *and* the button's state together, and `tick()` re-asserts them when the widget disagrees —
+  which is also why a hide *gesture* does not stick: the panel stays where the button says it is. The
+  no-signals case must leave the wish alone, or a source connecting later finds a sidebar the user never closed.
 - **`AdwOverlaySplitView:sidebar-width-fraction` is a 0..1 fraction of the window, whatever
   `sidebar-width-unit` says.** Setting a pixel count there (320) is a `GObject` critical, and it silently
   falls back to 0.25 — which reads as "the sidebar is mysteriously 560 px wide" on a wide window with no