WP search engine

Hi,
I added a simple on site search engine from the admin page>appearance>widget> added the search engine option and saved the changes.
Every tine I am trying to do a simple search, the search engine takes me out from my home page on WP to my companies website. I tried to find a solution in the forum, but nothing to point this problem.
there is a link to my home page: https://nightingalemusic.com/blog/

If you try to search for anything there, it will take you directly to my other site.

Any suggestions why it is happening?

Thanks.