The search behaves differently if fired from the homepage section and from the sidebar.
a. I am searching for the same term ‘eagle’. It shows 4 entries if I search from the frontpage denoted bt (2) here https://tinyurl.com/yxa6jrrw
and no results if searched from the filter in the sidebar https://tinyurl.com/y2a84yam again denoted by 2
It also gives the search term in the header bar
b. BUT the sidebar is empty (3). How to get the sidebar here?
c. The title should be Filter Trips not Filters Trips
Actually, you are confused with the term keyword used in the plugin.
Keyword is a taxonomy, kind of category used to group the trips as like the category. How it works is, you enter a new keyword from the Admin panel > Trips > Keyword and go to individual trip and assign that trips to that keyword.
Finally, when you search the keyword from the filter it will display the associated trips.
As from the front page, you just search the random word which is not a keyword and you tried the same word in that filter keyword which actually shows the trips associated with the certain keyword only.