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/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);
+		});
+	});
 });