If you did not figure out how to do this, I poked around and figured it out. There is a page of liquid coding that pops up when you edit your theme then search all of the liquid files using the term "search".
Online Store -> Themes --> Action --> Edit code ---> then search using the word "search"
At almost the top of the page there is a line of code that determines the number of products shown for search results. After copying and backing up the page, change the number and save the file.
This fixed the issue for me.
I am just a user, not a programmer so hopefully, I've explained this well enough. If it isn't easy and pretty close to what I've described for your theme, I'd close the window and back away slowly.
Good luck to you.