Header search box is wired to undefined handlers (query, handleSearch)

What's happening

packages/front-end/components/AppHeader.vue has a search input and button in the template:

<input type="search" ... v-model="query" ... />
<button type="submit" ... @click="handleSearch">

(lines 19 and 26), but neither query nor handleSearch are declared anywhere in the component's <script setup> block (line 73-83).

Impact

• Typing in the search box throws ReferenceError: query is not defined (strict-mode module scope) when the compiled v-model setter runs.
• Clicking the search button throws TypeError: handleSearch is not a function.
• The page itself loads fine (Vue only warns at render time — [Vue warn]: Property "query" was accessed during render but is not defined on instance — it doesn't throw until you actually interact with the input/button).

This means the header search feature is completely non-functional across every page (AppHeader is global).

Evidence

Confirmed via browser console during E2E test development this session. The E2E suite (packages/e2e/tests/main-workflow.spec.ts) deliberately avoids interacting with the search box so it doesn't trip over this unrelated, pre-existing bug.

Likely fix

Add const query = ref(""); and a handleSearch function (e.g. navigating to a search results route, or filtering the current product list) to AppHeader.vue's <script setup>.

Open packages/front-end/components/AppHeader.vue and inspect the <script setup> block around lines 73–83. Use packages/e2e/tests/main-workflow.spec.ts as the available test entry point, then verify that typing and submitting the header search no longer produce the reported console errors; the intended search-results behavior still needs clarification.