If you try to add WebP mime type from the BuddyBoss dashboard- Settings - Media - Manage Extensions (Documents), it will still not allow you to upload Webp images.

So, you add the below custom code on your child theme's function.php file, and it will enable the Webp image upload support to your website.

//add webp support
function enable_svg_upload( $upload_mimes ) {
    $upload_mimes['webp'] = 'image/webp';
    return $upload_mimes;
}
add_filter( 'upload_mimes', 'enable_svg_upload', 10, 1 );

You can also follow this video tutorial: https://drive.google.com/file/d/1XUVhqySVGnv8B9GOjpD2OFm5U0eINcsl/view?usp=sharing