Adding a search widget to a gutenberg block won’t use searchform.php

The widget blocks are not directly related to sidebar widgets. They are two different entities that happen to share the “widget” name and look similar in execution. The underlying code and method of implementation is different. To use your own form in a block you would need to create your own custom block or implement your form as a shortcode. We are encouraged to develop custom blocks instead of using shortcodes. Shortcodes are considered to be more for reverse compatibility. Either way will work though.
https://developer.www.ads-software.com/block-editor/tutorials/block-tutorial/writing-your-first-block-type/