Add "Search in bottom bar" to Settings

New Settings > Appearance toggle moves Search into the bottom bar and
out of the top bar, so there's only one search entry point on screen.
Tapping it pushes SearchView same as before - it's never highlighted,
since it isn't a real destination.

- Attached: Search becomes the row's last item, styled like any other
  tab but permanently idle.
- Floating: Search gets its own separate, always fully round satellite
  circle beside the bar instead.

Enabling it costs one regular tab: SettingsController.maxVisibleTabs
is now a dynamic getter (defaultMaxVisibleTabs - 1 while the toggle is
on) instead of the old flat constant, re-enforced immediately if the
user already has all 5 slots filled - the same cleanup path used for
a fresh install or an app update that added a new tab.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

.claude/context/styling.md

@@ -197,6 +197,12 @@ blocks are noted where they matter:
   with a `line` border instead of edge to edge (no opacity/blur knob
   either). The host `Scaffold` needs `extendBody: true` while it's active
   (`main.dart` already wires this off `SettingsController.bottomBarStyle`).
+  Settings' separate "Search in bottom bar" toggle
+  (`SettingsController.searchInBottomBar`) adds a never-highlighted Search
+  entry to either bar style (`NooBottomBar`'s `searchDestination`/
+  `onSearchTap`) and lowers `SettingsController.maxVisibleTabs` by one -
+  use that getter, not `defaultMaxVisibleTabs` from `models/app_tab.dart`,
+  anywhere that needs the *current* cap on regular tabs.
 - [`SyncedHeaderScaffold`](../../lib/widgets/synced_header_scaffold.dart) —
   the pull-to-sync `CustomScrollView` header with the persistent sync-status
   chip and pull-to-refresh gesture/spinner. Every screen (including