Thank you!
I actually found why this is happening. I was clicking randomly here and there, and it popped an input box, however there was no input element within the DOM tree in the inspector. So I looked at the source, and I found, that the span wrapper, where the plugin is placed, has a ‘contenteditable’ attribute. See it here: https://i.imgur.com/wfyl2pC.png
This basically allows the user to make changes to the content of that span element. I guess that is some sort of a widget container feature, or page builder feature. Maybe try containing the search shortcode within a different element/widget, that should resolve this issue. Unfortunately the search does not have any effect on this, as it is coming from the outside container.