Move filters into it's own component

What does this MR do and why?

3/5 Moving filters into their own sub-component to allow single-purpose component pattern

• Search Page vertical navigation search helper (merged)
• Search Page layout changes (merged)
• Move filters into their own component (merged) 👈 this MR
• Fix search helper vertical navigation JSON method (merged)
• Search Page Vue vertical navigation (merged)
  • Fix missing feature flag check in Vue vertical menu (merged)
  • Convert all Search Page RSpecs to support vertical search navigation

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This is a technical depth MR. No visible changes.

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Related to #293740 (closed)