Hi,
Thank you for the details, I think I know what the problem is. Generally, there is no connection between the search instances. But on the search results page, the search phrase is automatically printed to the search input. On your second search bar the search input is not visible, however the search phrase is still present – so when using the “Search” button it uses the previously entered search phrase along with the filters, yielding no results.
To resolve this, please try the following configuration on for the search button: https://i.imgur.com/0Lp4is0.png
(to redirect to Custom URL and the url should be ?s=)
This will reset the phrase when triggering a search via the second search bar.