The setup for refactoring styles in the left panel [without disabling Startup CSS]

What does this MR do?

The MR is the same as !62254 (merged), however without disabling the Startup CSS to prevent tests failures due to race condition between JS and CSS

Original Description

Sets the basis for refactoring the left-hand panel behind a feature flag. What this MR does:

CSS Changes:

• Creates a duplicate of contextual_sidebar.scss as contextual_sidebar_variant.scss
• Re-names original contextual_sidebar.scss into contextual_sidebar_base.scss
• Introduces the style hub to get both stylesheets' styles prefixed based on .sidebar-refactoring applied to the root element of the content part depending on the :sidebar_refactor feature flag

⚠ To test locally, please, enable the :sidebar_refactor feature flag for your local user. The flag is scoped to the user and is not global

Screenshots (strongly suggested)

master	This MR (with the flag enabled)

⚠ Keep in mind that the color changes in the panel are purely for the clear indication of the flag kicking in and will be replaced in the proper refactoring work.

Does this MR meet the acceptance criteria?

Conformity

• I have included a changelog entry, or it's not needed. (Does this MR need a changelog?)
• I have added/updated documentation, or it's not needed. (Is documentation required?)
• I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• I have added information for database reviewers in the MR description, or it's not needed. (Does this MR have database related changes?)
• 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.

Availability and Testing

• I have added/updated tests following the Testing Guide, or it's not needed. (Consider all test levels. See the Test Planning Process.)
• I have tested this MR in all supported browsers, or it's not needed.
• I have informed the Infrastructure department of a default or new setting change per definition of done, or it's not needed.

Related to #322680 (closed)