feat: Sicky search input for advanced styles section

[kof]

Description

1. What is this PR about (link the issue and add a short description)

Steps for reproduction

1. click button
2. expect xyz

Code Review

• hi @kof, I need you to do
  • conceptual review (architecture, feature-correctness)
  • detailed review (read every line)
  • test it on preview

Before requesting a review

• made a self-review
• added inline comments where things may be not obvious (the "why", not "what")

Before merging

• tested locally and on preview environment (preview dev login: 0000)
• updated test cases document
• added tests
• if any new env variables are added, added them to .env file

[johnsicili]

This is too problematic. That massive gap is the thing that needs to change imo. Unless search sets scroll back to top but IMO the blank space is the issue.

search.mp4

This pattern will be common btw... scroll for something, then decide to search