fix: improve data saving logic in search.js

[sy-records]

Summary

Related issue, if any:

Close #2674
Close #2689, Thanks @Bowl42
Close #2675, Thanks @kokovtsev

What kind of change does this PR introduce?

• Bugfix
• Feature
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no api changes)
• Build related changes
• Documentation content changes
• Other (please describe):

For any code change,

• Related documentation has been updated, if needed
• Related tests have been added or updated, if needed

Does this PR introduce a breaking change?

• Yes
• No

Tested in the following browsers:

• Chrome
• Firefox
• Safari
• Edge

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[paulhibbitts]

Thanks for taking on this PR @sy-records ! I had a difficult time in trying to replicate search failures in codesandbox with a broken page so I created two GitHub Pages test repos based on the example provided by @kokovtsev after verifying locally.

Search index test (RC) - search for 'ipsum' fails:
https://github.com/paulhibbitts/docsify-v5-search-index-RC
https://paulhibbitts.github.io/docsify-v5-search-index-RC/#/

Search index test (PR preview build) - search for 'ipsum' succeeds:
https://github.com/paulhibbitts/docsify-v5-search-index-PR
https://paulhibbitts.github.io/docsify-v5-search-index-PR/#/

Hope you can also confirm these tests.