Optimization of setup of Main Nav Layout, Contextual Sidebar and Fly Out Nav

What does this MR do?

Reduced the time on /explore for the layout init from 12ms to 2ms on my machine, on other pages even from 20ms to 3ms. This is even more on an actual build and especially machines with lower specs.

• Reduced unnecessary inits if there isn't any sidebar
• Deferred Inits which cause costly recalculate styles to requestIdle
• Fixed a cached lookup here and there
• Improved on saving the cookie only when necessary

Closes #56257 (closed)

What are the relevant issue numbers?

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated via this MR
• Tests added for this feature/bug
• Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• Security reports checked/validated by reviewer