feat(web-next): minimal authenticated shell home

Shell home for the platform-retrofit floor: a sign-in form (dev-seed
credentials) and a signed-in placeholder with sign-out. Both flows run
through the composed tRPC appRouter via server actions that own the
session cookie on the app side; the auth feature is untouched. Adds the
auth sign-in Playwright spec as the surviving e2e baseline and drops the
last demo-template metadata.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016j8z4VHjedXDTjEDNg7qHK

apps/web-next/src/app/layout.tsx

@@ -5,8 +5,8 @@ import { bindAll } from "../server/bind-production";
 import { Providers } from "./providers";
 
 export const metadata: Metadata = {
-  title: "Template — Next.js",
-  description: "Clean Architecture Monorepo Template",
+  title: "Veect",
+  description: "Veect",
 };
 
 export default async function RootLayout({

apps/web-next/src/app/page.tsx

@@ -1,11 +1,90 @@
+import { cookies } from "next/headers";
+import { SESSION_COOKIE } from "@repo/auth";
 import { bindAll } from "../server/bind-production";
+import { signInAction, signOutAction } from "../server/auth-actions";
 
-export default async function Home() {
+/**
+ * Shell home: the sign-in surface plus a minimal authenticated placeholder.
+ * The workspaces UI that replaces the placeholder arrives with the
+ * walking-skeleton PRD. Signed-in state is cookie presence only — session
+ * validation stays inside the auth feature and is exercised on sign-out.
+ */
+export default async function Home({
+  searchParams,
+}: {
+  searchParams: Promise<{ error?: string }>;
+}) {
   await bindAll();
+  const [cookieStore, params] = await Promise.all([cookies(), searchParams]);
+  const signedIn = cookieStore.has(SESSION_COOKIE);
 
   return (
-    <main className="mx-auto max-w-5xl px-6 py-8">
-      <h1 className="mb-4 text-2xl font-bold text-foreground">Veect</h1>
+    <main className="mx-auto flex min-h-screen w-full max-w-sm flex-col justify-center gap-6 px-6 py-8">
+      <h1 className="text-2xl font-bold text-foreground">Veect</h1>
+
+      {signedIn ? (
+        <section aria-label="Signed in" className="flex flex-col gap-4">
+          <p className="text-foreground">You are signed in.</p>
+          <form action={signOutAction}>
+            <button
+              type="submit"
+              className="rounded-md bg-primary px-4 py-2 text-sm font-medium text-primary-foreground"
+            >
+              Sign out
+            </button>
+          </form>
+        </section>
+      ) : (
+        <form
+          action={signInAction}
+          aria-label="Sign in"
+          className="flex flex-col gap-4"
+        >
+          <div className="flex flex-col gap-1">
+            <label
+              htmlFor="username"
+              className="text-sm font-medium text-foreground"
+            >
+              Username
+            </label>
+            <input
+              id="username"
+              name="username"
+              type="text"
+              autoComplete="username"
+              required
+              className="rounded-md border border-input bg-background px-3 py-2 text-foreground"
+            />
+          </div>
+          <div className="flex flex-col gap-1">
+            <label
+              htmlFor="password"
+              className="text-sm font-medium text-foreground"
+            >
+              Password
+            </label>
+            <input
+              id="password"
+              name="password"
+              type="password"
+              autoComplete="current-password"
+              required
+              className="rounded-md border border-input bg-background px-3 py-2 text-foreground"
+            />
+          </div>
+          {params.error === "invalid-credentials" ? (
+            <p role="alert" className="text-sm text-destructive">
+              Invalid username or password.
+            </p>
+          ) : null}
+          <button
+            type="submit"
+            className="rounded-md bg-primary px-4 py-2 text-sm font-medium text-primary-foreground"
+          >
+            Sign in
+          </button>
+        </form>
+      )}
     </main>
   );
 }