feat: sync active design to URL for refresh/share

Switching designs now reflects the active design id in the URL
(?design=<id>). A page refresh or shared link reopens that design;
an absent or unknown id falls back to the default design.

ha-relevant: no

frontend/src/utils/__tests__/designUrl.test.ts

@@ -0,0 +1,44 @@
+import { describe, it, expect, beforeEach } from 'vitest'
+import { getDesignIdFromUrl, setDesignIdInUrl } from '@/utils/designUrl'
+
+describe('designUrl', () => {
+  beforeEach(() => {
+    window.history.replaceState(null, '', '/')
+  })
+
+  it('returns null when no design param is present', () => {
+    expect(getDesignIdFromUrl()).toBeNull()
+  })
+
+  it('reads the design id from the URL', () => {
+    window.history.replaceState(null, '', '/?design=abc-123')
+    expect(getDesignIdFromUrl()).toBe('abc-123')
+  })
+
+  it('writes the design id into the URL without adding history', () => {
+    const before = window.history.length
+    setDesignIdInUrl('design-42')
+    expect(getDesignIdFromUrl()).toBe('design-42')
+    expect(window.history.length).toBe(before)
+  })
+
+  it('drops the param when passed null', () => {
+    setDesignIdInUrl('design-42')
+    setDesignIdInUrl(null)
+    expect(getDesignIdFromUrl()).toBeNull()
+    expect(window.location.search).toBe('')
+  })
+
+  it('preserves other query params when updating design', () => {
+    window.history.replaceState(null, '', '/?key=secret')
+    setDesignIdInUrl('design-42')
+    const params = new URLSearchParams(window.location.search)
+    expect(params.get('key')).toBe('secret')
+    expect(params.get('design')).toBe('design-42')
+  })
+
+  it('round-trips: written id is read back', () => {
+    setDesignIdInUrl('xyz')
+    expect(getDesignIdFromUrl()).toBe('xyz')
+  })
+})