Failing Unit Tests

[ZacharyRener]

Description of the Change

Unit tests and some e2e tests were failing due to a GitHub token format change, and a recent change to the Search Templates feature. This PR addresses both, and verifies that the tests pass again

Closes #205

How to test the Change

1. Open a PR with a whitespace change just to check the tests
2. Verify that the unit tests are failing, e.g. Trigger tests #204
3. Verify the failure error, e.g. https://github.com/10up/ElasticPressLabs/actions/runs/27837323447/job/82388278888?pr=204

Changelog Entry

Fixed - Tests were failing due to a GitHub token format change rollout and a search template issue.

Credits

Props @ZacharyRener

Checklist:

• I agree to follow this project's Code of Conduct.
• I have updated the documentation accordingly.
• I have added Critical Flows, Test Cases, and/or End-to-End Tests to cover my change.
• All new and existing tests pass.