I hope you are well today and thank you for your question.
The plugin provides functionality to display full-screen search clicking on the search icon as it is working on your website and not on clicking on the search form input field.
You have to develop custom code to display full-screen search clicking on the search form input field.
If you are not a developer then you can consider hiring a developer to develop it for you. You can hire a developer from any freelance site or WordPress agency.
You can also consider us to develop it for you using the form https://ivorysearch.com/custom-work/
Best regards,
Ivory Search Support