Initial commit: EGBE chatbot template

Stripped from vercel/chatbot (Apache 2.0):
- Dropped @vercel/* packages and AI Gateway
- Removed artifacts feature (code/text/sheet/image side panel)
- Switched AI provider to @ai-sdk/openai-compatible -> EGBE LiteLLM
- Replaced Vercel Blob upload with data URLs
- Dropped Redis resumable streams and rate limiter (in-memory now)
- Added Dockerfile (Next.js standalone) + entrypoint that runs migrations
- Wired DATABASE_URL, EGBE_AI_API_URL/KEY, NEXT_PUBLIC_BASE_URL for app-deploy.sh

components/chat/auth-form.tsx

@@ -0,0 +1,53 @@
+import Form from "next/form";
+
+import { Input } from "../ui/input";
+import { Label } from "../ui/label";
+
+export function AuthForm({
+  action,
+  children,
+  defaultEmail = "",
+}: {
+  action: NonNullable<
+    string | ((formData: FormData) => void | Promise<void>) | undefined
+  >;
+  children: React.ReactNode;
+  defaultEmail?: string;
+}) {
+  return (
+    <Form action={action} className="flex flex-col gap-4">
+      <div className="flex flex-col gap-2">
+        <Label className="font-normal text-muted-foreground" htmlFor="email">
+          Email
+        </Label>
+        <Input
+          autoComplete="email"
+          autoFocus
+          className="h-10 rounded-lg border-border/50 bg-muted/50 text-sm transition-colors focus:border-foreground/20 focus:bg-muted"
+          defaultValue={defaultEmail}
+          id="email"
+          name="email"
+          placeholder="you@someo.ne"
+          required
+          type="email"
+        />
+      </div>
+
+      <div className="flex flex-col gap-2">
+        <Label className="font-normal text-muted-foreground" htmlFor="password">
+          Password
+        </Label>
+        <Input
+          className="h-10 rounded-lg border-border/50 bg-muted/50 text-sm transition-colors focus:border-foreground/20 focus:bg-muted"
+          id="password"
+          name="password"
+          placeholder="&bull;&bull;&bull;&bull;&bull;&bull;&bull;&bull;"
+          required
+          type="password"
+        />
+      </div>
+
+      {children}
+    </Form>
+  );
+}