functions.php

<?php 

function add_file_and_ext_webp( $types, $file, $filename, $mimes ) {
    if ( false !== strpos( $filename, '.webp' ) ) {
        $types['ext'] = 'webp';
        $types['type'] = 'image/webp';
    }

    return $types;
}

add_filter( 'wp_check_filetype_and_ext', 'add_file_and_ext_webp', 10, 4 );


function add_mime_types_webp( $mimes ) {
    $mimes['webp'] = 'image/webp';

  return $mimes;
  
}

add_filter( 'upload_mimes', 'add_mime_types_webp' );