Refactor end-to-end test to make it more robust

What does this MR do?

Refactor end-to-end test to make it more robust, and simpler.

Closes #36688 (closed).

The removed expectation is based on #39208 (comment 259377790).

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• [-] Separation of EE specific content