wire the output dock into the layout — toggle, tabs, persistence (T-54)

The D-87 bottom dock, end to end. New Slots.dock in the classic preset
(hidden by default); RootLayout renders it full-width above the status bar
when open, capped at half the window so Claude stays largest (the D-47
amendment). LogRing now lives on KernelServices (boot tees the kernel logger
into it; main.dart also tees the IPC/MCP logger), so the dock shows logs from
every subsystem.

OutputExtension contributes the Output tab, the merged health/toggle
status-bar widget (green check when clean, warn/error counts otherwise) that
replaces the old ipc-status item, and the dock.toggle command (Ctrl+J).
Problems moves out of the sidebar into the dock. open/height persist per
workspace via the default-layout extension.

Drag-resize of the dock height is deferred (DragResizeHandle needs a dock
sign case); height is the persisted default for now. Boot verified via
testmode; full suite green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lib/builtin/problems/src/extension.dart

@@ -1,7 +1,6 @@
 import 'package:clide/builtin/problems/src/problems_view.dart';
 import 'package:clide/extension/extension.dart';
 import 'package:clide/kernel/kernel.dart';
-import 'package:clide/widgets/widgets.dart';
 
 class ProblemsExtension extends ClideExtension {
   @override
@@ -15,11 +14,12 @@ class ProblemsExtension extends ClideExtension {
 
   @override
   List<ContributionPoint> get contributions => [
+        // Moved out of the sidebar into the bottom dock (D-87): no duplication,
+        // and the dock's width fits `severity · file:line · message` rows.
         TabContribution(
           id: 'problems.panel',
-          slot: Slots.sidebar,
+          slot: Slots.dock,
           title: 'Problems',
-          icon: PhosphorIcons.warningCircle,
           titleKey: 'tab.title',
           i18nNamespace: id,
           priority: -50,