Fix a flaky feature spec

What does this MR do?

Since a branch deletion happens in the background, we need to wait for all requests to be done before asserting for the branch deletion.

In addition, in the case the test is retried because the branch deletion is taking too long, it's a best practice to use a new project object since branches are not recreated if when using set (since set only reload DB attributes).

Using let is safer and makes the test idempotent.

Does this MR meet the acceptance criteria?

Conformity

• Code review guidelines
• Merge request performance guidelines
• Style guides
• Separation of EE specific content

Closes #12613 (closed).