Fix avatar menu's missing border and put the tab title beside search

- The avatar menu card's border was going missing wherever an opaque
  row sat against it (every corner but the header's) - a Container
  combining `border` with its own `clipBehavior` paints the border as
  part of the outer decoration, then the clipped child on top right up
  to the same boundary, with no gap for the border's stroke to show
  through. Fixed with the standard pattern: no clipBehavior on the
  bordered Container, a 1px-inset ClipRRect around the filled, clipped
  content instead.
- NooTopBar.androidTitleTrailing (renamed from androidTitleReplacement)
  now sits beside the tab title instead of replacing it - the title
  keeps its natural width (Flexible, ellipsizing only if truly out of
  room) with the inline search bar taking the remaining space to its
  right, rather than the title disappearing whenever search moves into
  the top bar.

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

.claude/context/styling.md

@@ -245,11 +245,23 @@ blocks are noted where they matter:
   near-black `bg` (a dark, diffuse shadow needs real density close to the
   edge to be visible against an already-dark backdrop), so a second,
   tighter, more opaque contact shadow underneath it gives real elevation
-  in both themes. Also added `NooTopBar.androidTitleReplacement`: Android has no
-  large title to put a second search row under the way iOS's `search:`
-  slot does, so an inline search bar (`AppTopBar` passes a plain
-  `ShellSearchLauncher()` when search isn't in the bottom bar) replaces the
-  title in its flexible slot instead of sitting beside it as a bare icon.
+  in both themes. The card's border can go missing wherever an opaque row
+  sits against it too (every corner but the header's, which has no
+  full-bleed fill of its own) if a `Container` combines `border` with its
+  own `clipBehavior` - that paints the border as part of the *outer*
+  decoration, then the clipped child on top right up to the same boundary,
+  with no gap for the border's own stroke to show through. Fixed the same
+  way any bordered-and-clipped `Container` should be: no `clipBehavior` on
+  the bordered `Container` itself, and a 1px-inset `ClipRRect` (radius
+  reduced by that same 1px) around the filled, clipped content instead, so
+  it never paints over the border. Also added
+  `NooTopBar.androidTitleTrailing`: Android has no large title to put a
+  second search row under the way iOS's `search:` slot does, so an inline
+  search bar (`AppTopBar` passes a plain `ShellSearchLauncher()` when
+  search isn't in the bottom bar) sits to the title's own right in that
+  flexible slot - `Flexible`, not `Expanded`, so the title still shrinks/
+  ellipsizes if there's truly no room but doesn't claim more than it needs
+  otherwise - instead of the title being replaced by it.
 - [`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