For #27522: Re-enabled and added search group UI tests

[sv-ohorvath]

Found a workaround to avoid the tabs tray, so the search group tests can be re-enabled, and added some new ones to improve the coverage of the Search suite.

Pull Request checklist

• Tests: This PR includes thorough tests or an explanation of why it does not
• Screenshots: This PR includes screenshots or GIFs of the changes made or an explanation of why it does not
• Accessibility: The code in this PR follows accessibility best practices or does not include any user facing features. In addition, it includes a screenshot of a successful accessibility scan to ensure no new defects are added to the product.

QA

• [] QA Needed

To download an APK when reviewing a PR (after all CI tasks finished running):

1. Click on Checks at the top of the PR page.
2. Click on the firefoxci-taskcluster group on the left to expand all tasks.
3. Click on the build-debug task.
4. Click on View task in Taskcluster in the new DETAILS section.
5. The APK links should be on the right side of the screen, named for each CPU architecture.

GitHub Automation

Fixes #27522