It looks like you have an issue with the HTML minification. For example, when I log in, and check the page source, the page elements look perfectly fine, but when cached, it is completely broken.
For example:
– Incorrectly “modified” input element within the search: https://i.imgur.com/pHthP2Q.png
– Correct (when logged in): https://i.imgur.com/Ds9jyVB.png
The error console is also full of error reports: https://i.imgur.com/WsrjB5l.png
Unfortunately these issues are not generated by the search plugin. It does not work because of these issues. I believe the most important one is the minification/HTML optimization related problem. I am 99% sure that the incorrect minfication causes all the issues.