🐛 fix(lightwrite): add LightWriteLogo to shared-branding

- Add lightwrite to AppId type
- Add lightwrite branding config (orange theme, music note icon)
- Create LightWriteLogo.svelte component
- Update login/register pages to use proper logo component
- Fixes type-check errors in @lightwrite/web

apps/lightwrite/apps/web/src/routes/(auth)/login/+page.svelte

@@ -4,13 +4,9 @@
 	import { browser } from '$app/environment';
 	import { LoginPage } from '@manacore/shared-auth-ui';
 	import { getLoginTranslations } from '@manacore/shared-i18n';
+	import { LightWriteLogo } from '@manacore/shared-branding';
 	import { authStore } from '$lib/stores/auth.svelte';
 
-	// Simple LightWrite Logo component
-	function LightWriteLogo() {
-		return null; // Will use appName text instead
-	}
-
 	// Get redirect URL from query params or sessionStorage
 	const redirectTo = $derived.by(() => {
 		const queryRedirect = $page.url.searchParams.get('redirectTo');

apps/lightwrite/apps/web/src/routes/(auth)/register/+page.svelte

@@ -3,13 +3,9 @@
 	import { browser } from '$app/environment';
 	import { RegisterPage } from '@manacore/shared-auth-ui';
 	import { getRegisterTranslations } from '@manacore/shared-i18n';
+	import { LightWriteLogo } from '@manacore/shared-branding';
 	import { authStore } from '$lib/stores/auth.svelte';
 
-	// Simple LightWrite Logo component
-	function LightWriteLogo() {
-		return null; // Will use appName text instead
-	}
-
 	// Get redirect URL from sessionStorage
 	const redirectTo = $derived.by(() => {
 		if (browser) {