Replace v-show on Designs toolbar with d-none class

What does this MR do?

In !22516 (merged) I've fixed the disabling of Delete Selected button after deleting all designs. Unfortunately, v-show directive now collides with Bootstrap-Vue d-flex utility class:

This MR replaces v-show with conditional d-none class to prevent the collision and adds a proper unit test to prevent this regression in the future.

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

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers

Related issue: #118627 (closed)