[Web][Docs] Search bar content without search string in v5 documentation page

• I have searched the issues of this repository and believe that this is not a duplicate.

Summary 💡

• Add a "How to search effectively" with more space or always show on top. (Idea from @siriwatknp https://github.com/mui-org/material-ui/issues/28415#issuecomment-925009375)
• (misbehavior?) In the search bar, to trigger the search guide(or default introduction), we need to type something then delete them all to show the search guide. See example.
• Remove some of current content.
• The issue was initially mentioned here https://github.com/mui-org/material-ui/issues/28415
• This issue is to separate different topics.

Examples 🌈

I would like to have some (limited) access to your prototyping tool like https://siriwatknp.github.io/mui-docsearch/ to make it clearer and easier during the communication.

• Old correct behavior
  

• Current (mis-)behavior
  

• Expected behavior
  

• In Expected behavior, that ugly thing should be a better designed button acts like a search result.

Motivation 🔦

Usability: to make search easier

Start by reviewing the v5 documentation page search bar behavior, the linked original issue, and the attached old, current, and expected examples. Determine the agreed empty-search guide and content changes before editing. Done means the empty search state shows the intended guide or result-like button without requiring typed text to be deleted.