I have my own code to insert on the site, how to change the search engine for the site
A custom search engine can be added to Q2A by creating a search module; please read the documentation for more details. The first two steps of the plugin tutorial describe how to create a widget module but it might give you hints on how to create a search module as well.
After it's defined, it'll appear in the drop-down menu next to the 'Use search module:' option, which appears under 'Admin' > 'Lists' page.
I hope it helps.
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April 20, 2021: Q2A 1.8.6 released!