feat: Search for advanced section in style panel

[kof]

#4805

Description

1. start searching
2. abort with esc
3. try in default as well as in advanced mode
4. try with recent changes and without

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