Problem:
After enabling the Layout Plugin and its genesis integration plugin, you notice that the Genesis native Search function is broken and returns the wrong posts.
Solution:
This search is not broken. Broken means, it is not working. Your Search is since Layouts is enabled, returning other posts than you expected.
This is because "Layout for Search Results" is assigned to the Search Archive now, by default.
If you disable / delete Layouts and the Integration, you can right now not change this.
Please (if uninstalled) try to re-install the required Plugins and go to Layouts > Layouts, find and click on "Change Layout Use", there you should uncheck "Search" from Archive part.
This will bring back the standard Genesis search function.
Beware that the default layout shipped with the integration is a dummy layout with 3 dummy (non-existing posts) to demonstrate only how it should look and the instructions to achieve that.
If you want, you can also keep Layouts and Genesis integration, and customize the Archive Cell that you will find in that Layout.
You can use the WordPress Archive Cell to display the actual posts loop.
Relevant Documentation:
https://toolset.com/documentation/user-guides/normal-vs-archive-views/
https://toolset.com/documentation/user-guides/wordpress-archive-cell/
https://toolset.com/documentation/user-guides/layouts-genesis-integration/