feat(auth): add signup page with form action

Composes BrandPanel + SignupForm in responsive split layout.
Server action POSTs to /v1/auth/signup and redirects to
/household/setup on success.

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

frontend/src/routes/(public)/signup/+page.server.ts

@@ -0,0 +1,23 @@
+import { redirect, fail } from '@sveltejs/kit';
+import { apiClient } from '$lib/server/api';
+import type { Actions } from './$types';
+
+export const actions = {
+	default: async ({ request, fetch }) => {
+		const formData = await request.formData();
+		const displayName = formData.get('displayName') as string;
+		const email = formData.get('email') as string;
+		const password = formData.get('password') as string;
+
+		const api = apiClient(fetch);
+		const { data, error } = await api.POST('/v1/auth/signup', {
+			body: { displayName, email, password }
+		});
+
+		if (error) {
+			return fail(400, { error: 'Registrierung fehlgeschlagen. Bitte versuche es erneut.' });
+		}
+
+		redirect(303, '/household/setup');
+	}
+} satisfies Actions;

frontend/src/routes/(public)/signup/+page.svelte

@@ -0,0 +1,14 @@
+<script lang="ts">
+	import BrandPanel from '$lib/auth/BrandPanel.svelte';
+	import SignupForm from '$lib/auth/SignupForm.svelte';
+</script>
+
+<!-- Mobile: stacked, Desktop: side by side -->
+<div class="flex min-h-screen flex-col md:flex-row">
+	<BrandPanel />
+	<div class="flex flex-1 flex-col justify-center px-[20px] py-[24px] md:px-[56px] md:py-[48px]">
+		<div class="max-w-[380px]">
+			<SignupForm />
+		</div>
+	</div>
+</div>

frontend/src/routes/(public)/signup/page.server.test.ts

@@ -0,0 +1,85 @@
+import { describe, it, expect, vi, beforeEach } from 'vitest';
+
+vi.mock('$env/dynamic/private', () => ({
+	env: { BACKEND_URL: 'http://localhost:8080' }
+}));
+
+const mockPost = vi.fn();
+vi.mock('$lib/server/api', () => ({
+	apiClient: () => ({ POST: mockPost })
+}));
+
+describe('signup form action', () => {
+	let actions: any;
+
+	beforeEach(async () => {
+		mockPost.mockReset();
+		const mod = await import('./+page.server');
+		actions = mod.actions;
+	});
+
+	function createRequest(formData: Record<string, string>) {
+		const fd = new FormData();
+		for (const [key, value] of Object.entries(formData)) {
+			fd.append(key, value);
+		}
+		return {
+			request: { formData: () => Promise.resolve(fd) },
+			fetch: vi.fn(),
+			cookies: { get: vi.fn(), set: vi.fn() }
+		} as any;
+	}
+
+	it('calls POST /v1/auth/signup with form data', async () => {
+		mockPost.mockResolvedValue({ data: { data: { id: '123' } }, error: undefined });
+
+		try {
+			await actions.default(createRequest({
+				displayName: 'Sarah',
+				email: 'sarah@example.com',
+				password: 'password123'
+			}));
+		} catch {
+			// redirect throws
+		}
+
+		expect(mockPost).toHaveBeenCalledWith('/v1/auth/signup', {
+			body: {
+				displayName: 'Sarah',
+				email: 'sarah@example.com',
+				password: 'password123'
+			}
+		});
+	});
+
+	it('redirects to /household/setup on success', async () => {
+		mockPost.mockResolvedValue({ data: { data: { id: '123' } }, error: undefined });
+
+		try {
+			await actions.default(createRequest({
+				displayName: 'Sarah',
+				email: 'sarah@example.com',
+				password: 'password123'
+			}));
+			expect.unreachable();
+		} catch (e: any) {
+			expect(e.status).toBe(303);
+			expect(e.location).toBe('/household/setup');
+		}
+	});
+
+	it('returns fail with error message on API error', async () => {
+		mockPost.mockResolvedValue({
+			data: undefined,
+			error: { status: 409, message: 'Email already registered' }
+		});
+
+		const result = await actions.default(createRequest({
+			displayName: 'Sarah',
+			email: 'sarah@example.com',
+			password: 'password123'
+		}));
+
+		expect(result.status).toBe(400);
+	});
+});