refactor: replace Fomantic search module with first-party code (#37443)

- Replace fomantic `search` code with minimal first-party code
- Added a small fix to vertically align search box and search button
- Manually tested all search forms.
- Add `errorName` helper, similar to `errorMessage`.

Signed-off-by: silverwind <me@silverwind.io>
Co-authored-by: Claude (Opus 4.7) <noreply@anthropic.com>

tests/e2e/org.test.ts

@@ -1,5 +1,5 @@
 import {test, expect} from '@playwright/test';
-import {login, apiDeleteOrg, randomString} from './utils.ts';
+import {login, apiCreateOrg, apiCreateTeam, apiCreateUser, apiDeleteOrg, randomString} from './utils.ts';
 
 test('create an organization', async ({page}) => {
   const orgName = `e2e-org-${randomString(8)}`;
@@ -11,3 +11,24 @@ test('create an organization', async ({page}) => {
   // delete via API because of issues related to form-fetch-action
   await apiDeleteOrg(page.request, orgName);
 });
+
+test('add team member search', async ({page, request}) => {
+  const orgName = `team-add-${randomString(8)}`;
+  const teamName = `team-add-${randomString(8)}`;
+  const userName = `team-add-${randomString(8)}`;
+
+  await Promise.all([
+    (async () => {
+      await apiCreateOrg(request, orgName);
+      await apiCreateTeam(request, orgName, teamName);
+    })(),
+    apiCreateUser(request, userName),
+    login(page),
+  ]);
+
+  await page.goto(`/org/${orgName}/teams/${teamName}`);
+  const input = page.locator('#search-user-box input.prompt');
+  await input.fill(userName.slice(-6));
+  const result = page.locator('#search-user-box .results .result').first();
+  await expect(result).toContainText(userName);
+});