BUG: E2e tests with WP 6.3

### Describe the bug

Some of our e2e tests are not working with WP 6.3

### Steps to Reproduce

Check the e2e test results.

### Screenshots, screen recording, code snippet

_No response_

### Environment information

_No response_

### WordPress and ElasticPress information

_No response_

### Code of Conduct

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