ui: the sidebar's tabs become one dock; Measure and Signals by keyboard section; session keeps the dock's state

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

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

@@ -23,10 +23,11 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   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 —
+  `set_active`), `update_side_visibility()` is the single place that turns that wish into the panel's visibility
+  and "are there signals" into the dock's *sensitivity* (the button stays sensitive), and `tick()` re-asserts both 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.
+  The wish is the session's `dock` key: a change of it (not a program's own write, and not a restore) schedules a save.
 - **`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