test(docs): make search and nav e2e tests hydration-aware (#551)

The docs e2e suite clicked navbar and sidebar controls before Vue hydrated the
multi-locale bundle, so the clicks were swallowed. That raced the Pagefind
search open (filed as #551), the appearance toggle, and the homepage and
sidebar navigation tests. The old search tests also matched an input
placeholder the config overrides, so they failed against a working build.

Add a waitForHydration helper (gates on #app.__vue_app__, set inside Vue's
app.mount()) and an openDocsSearch helper, and route the affected tests through
them. Search itself was never broken; this change is test-only. Docs e2e suite
is green (43/43).

Closes #551

tests/e2e-docs/homepage.spec.ts

@@ -1,8 +1,12 @@
 import { expect, test } from "@playwright/test";
+import { waitForHydration } from "./helpers";
 
 test.describe("docs homepage (Two Doors)", () => {
   test.beforeEach(async ({ page }) => {
     await page.goto("/");
+    // Some tests click nav/chip links, which route client-side; wait for Vue to
+    // hydrate first so the click isn't swallowed (the #551 pre-hydration race).
+    await waitForHydration(page);
   });
 
   test("title contains SnapOtter", async ({ page }) => {