Add Settings menu to new Sidebar

What does this MR do?

In this MR, we're refactoring the Settings menu. We're moving it from being a partial rendered menu to an object-driven menu, like all the menus in the project sidebar.

For that, we're just introducing a new object to store the menu info and removing the related info from the menu partial.

Screenshots or Screencasts (strongly suggested)

Does this MR meet the acceptance criteria?

Conformity

• I have included changelog trailers, or none are needed. (Does this MR need a changelog?)
• I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• I have self-reviewed this MR per code review guidelines.
• This MR does not harm performance, or I have asked a reviewer to help assess the performance impact. (Merge request performance guidelines)
• I have followed the style guides.
• This change is backwards compatible across updates, or this does not apply.

Related to #328514 (closed)