Consolidate all study-dependent routes and UI

- Remove global experiments and plugins routes; redirect to study-scoped
  pages
- Update sidebar navigation to separate platform-level and study-level
  items
- Add study filter to dashboard and stats queries
- Refactor participants, trials, analytics pages to use new header and
  breadcrumbs
- Update documentation for new route architecture and migration guide
- Remove duplicate experiment creation route
- Upgrade Next.js to 15.5.4 in package.json and bun.lock

src/app/(dashboard)/experiments/new/page.tsx

@@ -1,5 +0,0 @@
-import { ExperimentForm } from "~/components/experiments/ExperimentForm";
-
-export default function NewExperimentPage() {
-  return <ExperimentForm mode="create" />;
-}

src/app/(dashboard)/experiments/page.tsx

@@ -1,10 +1,65 @@
-import { ExperimentsDataTable } from "~/components/experiments/experiments-data-table";
-import { StudyGuard } from "~/components/dashboard/study-guard";
+"use client";
+
+import { useEffect } from "react";
+import { useRouter } from "next/navigation";
+import Link from "next/link";
+import { FlaskConical, ArrowRight } from "lucide-react";
+import { Button } from "~/components/ui/button";
+import {
+  Card,
+  CardContent,
+  CardDescription,
+  CardHeader,
+  CardTitle,
+} from "~/components/ui/card";
+import { useStudyContext } from "~/lib/study-context";
+
+export default function ExperimentsRedirect() {
+  const router = useRouter();
+  const { selectedStudyId } = useStudyContext();
+
+  useEffect(() => {
+    // If user has a selected study, redirect to study experiments
+    if (selectedStudyId) {
+      router.replace(`/studies/${selectedStudyId}/experiments`);
+    }
+  }, [selectedStudyId, router]);
 
-export default function ExperimentsPage() {
   return (
-    <StudyGuard>
-      <ExperimentsDataTable />
-    </StudyGuard>
+    <div className="flex min-h-[60vh] items-center justify-center p-4">
+      <Card className="w-full max-w-md">
+        <CardHeader className="text-center">
+          <div className="mx-auto mb-4 flex h-16 w-16 items-center justify-center rounded-full bg-blue-50">
+            <FlaskConical className="h-8 w-8 text-blue-500" />
+          </div>
+          <CardTitle className="text-2xl">Experiments Moved</CardTitle>
+          <CardDescription>
+            Experiment management is now organized by study for better
+            workflow organization.
+          </CardDescription>
+        </CardHeader>
+        <CardContent className="space-y-4">
+          <div className="text-muted-foreground space-y-2 text-center text-sm">
+            <p>To manage experiments:</p>
+            <ul className="space-y-1 text-left">
+              <li>• Select a study from your studies list</li>
+              <li>• Navigate to that study&apos;s experiments page</li>
+              <li>• Create and manage experiment protocols for that specific study</li>
+            </ul>
+          </div>
+          <div className="flex flex-col gap-2 pt-4">
+            <Button asChild className="w-full">
+              <Link href="/studies">
+                <ArrowRight className="mr-2 h-4 w-4" />
+                Browse Studies
+              </Link>
+            </Button>
+            <Button asChild variant="outline" className="w-full">
+              <Link href="/dashboard">Go to Dashboard</Link>
+            </Button>
+          </div>
+        </CardContent>
+      </Card>
+    </div>
   );
 }