Resolve "Simplify editing shortcuts to projects and groups"

What does this MR do and why?

Resolves #406270 (closed) by deleting the editMode code and always showing a ➖ icon to remove a "frequently visited project/group".

Screenshots or screen recordings

header	After
recording_1681988512	recording_1681988361

How to set up and validate locally

• Feature.enable(:super_sidebar_nav) and toggle on the "New navigation" in your user dropdown.
• On any page, open the context switcher.
• In there, delete a frequently visited project and group.

MR acceptance checklist

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• I have evaluated the MR acceptance checklist for this MR.