In the Settings panel, you can vary the search bar style: Set the background color of the widget, close and search icons, etc. The widget style and position can be modified as well.
To use another icon, simply upload an image to the Content panel of the block. Also, you can add a tooltip to the input field and specify pre-selected search suggestions that will immediately take users to results.
📌 To enable the search function, select the box "Enable internal website search" in Site Settings → More.