feat: add schema browser sidebar and app layout

Add SchemaTree with database/schema/category hierarchy, Sidebar with
search, Toolbar, TabBar, StatusBar, and full app layout with
resizable panels.

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

src/components/layout/Sidebar.tsx

@@ -0,0 +1,27 @@
+import { useState } from "react";
+import { Input } from "@/components/ui/input";
+import { SchemaTree } from "@/components/schema/SchemaTree";
+import { Search } from "lucide-react";
+
+export function Sidebar() {
+  const [search, setSearch] = useState("");
+
+  return (
+    <div className="flex h-full flex-col bg-card">
+      <div className="p-2">
+        <div className="relative">
+          <Search className="absolute left-2 top-1/2 h-3.5 w-3.5 -translate-y-1/2 text-muted-foreground" />
+          <Input
+            placeholder="Search objects..."
+            className="h-7 pl-7 text-xs"
+            value={search}
+            onChange={(e) => setSearch(e.target.value)}
+          />
+        </div>
+      </div>
+      <div className="min-h-0 flex-1 overflow-y-auto overflow-x-hidden">
+        <SchemaTree />
+      </div>
+    </div>
+  );
+}