fix(nav): use segment-boundary route matching to prevent false positives

Extracts isActiveRoute() into shared nav module. Matches exact path
or path + '/' prefix, preventing /settings from matching /settings-advanced.

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

frontend/src/lib/nav/DesktopSidebar.svelte

@@ -1,6 +1,6 @@
 <script lang="ts">
 	import { page } from '$app/stores';
-	import { desktopNavSections } from './nav';
+	import { desktopNavSections, isActiveRoute } from './nav';
 
 	let { appName, householdName }: { appName: string; householdName: string } = $props();
 </script>
@@ -24,7 +24,7 @@
 				{section.title}
 			</p>
 			{#each section.items as item (item.href)}
-				{@const active = $page.url.pathname.startsWith(item.href)}
+				{@const active = isActiveRoute(item.href, $page.url.pathname)}
 				<a
 					href={item.href}
 					aria-current={active ? 'page' : undefined}

frontend/src/lib/nav/MobileTabBar.svelte

@@ -1,6 +1,6 @@
 <script lang="ts">
 	import { page } from '$app/stores';
-	import { mobileNavItems } from './nav';
+	import { mobileNavItems, isActiveRoute } from './nav';
 </script>
 
 <nav
@@ -8,7 +8,7 @@
 	class="fixed bottom-0 w-full flex justify-around bg-white border-t pb-[env(safe-area-inset-bottom,20px)] md:hidden"
 >
 	{#each mobileNavItems as item (item.href)}
-		{@const active = $page.url.pathname.startsWith(item.href)}
+		{@const active = isActiveRoute(item.href, $page.url.pathname)}
 		<a
 			href={item.href}
 			aria-current={active ? 'page' : undefined}

frontend/src/lib/nav/TabletNavBar.svelte

@@ -1,6 +1,6 @@
 <script lang="ts">
 	import { page } from '$app/stores';
-	import { mobileNavItems } from './nav';
+	import { mobileNavItems, isActiveRoute } from './nav';
 </script>
 
 <nav
@@ -8,7 +8,7 @@
 	class="hidden md:flex lg:hidden gap-2 items-center p-2"
 >
 	{#each mobileNavItems as item (item.href)}
-		{@const active = $page.url.pathname.startsWith(item.href)}
+		{@const active = isActiveRoute(item.href, $page.url.pathname)}
 		<a
 			href={item.href}
 			aria-current={active ? 'page' : undefined}

frontend/src/lib/nav/nav.test.ts

@@ -1,5 +1,5 @@
 import { describe, it, expect } from 'vitest';
-import { mobileNavItems, desktopNavSections } from './nav';
+import { mobileNavItems, desktopNavSections, isActiveRoute } from './nav';
 
 describe('nav config', () => {
 	describe('mobileNavItems', () => {
@@ -39,4 +39,22 @@ describe('nav config', () => {
 			expect(labels).toEqual(['Mitglieder', 'Einstellungen']);
 		});
 	});
+
+	describe('isActiveRoute', () => {
+		it('matches exact route', () => {
+			expect(isActiveRoute('/planner', '/planner')).toBe(true);
+		});
+
+		it('matches sub-route', () => {
+			expect(isActiveRoute('/planner', '/planner/week')).toBe(true);
+		});
+
+		it('does not match route with similar prefix', () => {
+			expect(isActiveRoute('/settings', '/settings-advanced')).toBe(false);
+		});
+
+		it('does not match unrelated route', () => {
+			expect(isActiveRoute('/planner', '/recipes')).toBe(false);
+		});
+	});
 });

frontend/src/lib/nav/nav.ts

@@ -16,6 +16,10 @@ export const mobileNavItems: NavItem[] = [
 	{ href: '/settings', label: 'Einstellungen', icon: 'settings' }
 ];
 
+export function isActiveRoute(href: string, pathname: string): boolean {
+	return pathname === href || pathname.startsWith(href + '/');
+}
+
 export const desktopNavSections: NavSection[] = [
 	{
 		title: 'Plan',