I think what you are after is the option “Run search: When criteria is changed” which is available in the “Search Settings” accessible from the kebab menu (three dots) on the search bar:

It is a method of development.
After pressing the search button on this search panel, I want to register data in another table. Are there any settings that apply to projections or clients?

What do you mean by “Register data”? What exactly is it that you want to do?

Simply put, I want to add some processing after pressing the search button.

You can add processing whenever data is loaded for the projection entityset via BPA (Business Process Automation)/Workflows by adding a Projection Action on CRUD action “READ”:

 

That’s probably the closest you can get with your requirement.

@Jonas Feigl 

Thank you for your support.  I will try this.