docs(src): fix Sidebar filter and Intro editors

[levithomason]

Introduction

The recent editor updates had a negative impact on the introduction page.

Before

After

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Sidebar Filter

Before

After

• Moved the ad to the bottom of the sidebar 👍
• Fixed instant search capability (Press "/" to filter)
• Improved UX and style of filter behavior

[codecov-io]

Codecov Report

Merging #3044 into master will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master    #3044   +/-   ##
=======================================
  Coverage   99.96%   99.96%           
=======================================
  Files         163      163           
  Lines        2738     2738           
=======================================
  Hits         2737     2737           
  Misses          1        1

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