Improvements to new entry dropdowns in Web IDE

What does this MR do?

Improves the design of the new entry dropdown in the folder rows & in the table header. The table header is now just a row of buttons instead of a dropdown. For the dropdown, each row now has an icon next to the text.

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conform by the code review guidelines
  • Has been reviewed by a UX Designer
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
  • Has been reviewed by a Database specialist
• Conform by the merge request performance guides
• Conform by the style guides
• Conform by the database guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

Part of #44845 (closed)