fix: TOC filter value is not shared between pages

[filzrev]

This PR intended to fix issue reported by #9791.

On current implementation.
TOC filtering text value is not propagated between pages as expected.
And It seems to work as following behaviors.

• tocFilterUrl is always set as empty string.
• tocFilter value is set on textbox update. But it's reset on every page loading.

This PR change behaviors.

1. tocFilterUrl value is updated if existing value is empty or another TOC URL is referenced.
2. tocFilter value is reset to empty string when following conditions.
   2.1. When navigating to docfx site (tocFilterUrl === '')
   2.2. When navigated page referencing another TOC. (tocFilterUrl !== tocUrl.toString()) ([Bug] Filter in TOC not reset #9117)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 78.96%. Comparing base (fe673ec) to head (5bf5cb3).
Report is 146 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9912      +/-   ##
==========================================
+ Coverage   74.31%   78.96%   +4.64%     
==========================================
  Files         536      538       +2     
  Lines       23189    23316     +127     
  Branches     4056     4047       -9     
==========================================
+ Hits        17234    18412    +1178     
+ Misses       4853     3775    -1078     
- Partials     1102     1129      +27     

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