Modify upload directory to use post category slug in file path on multisite installation

try this:

function add_taxonomy_to_upload_dir( $upload ) {
    if ( isset( $_REQUEST['post'] ) ) {
        // wp-json/wp/v2/media
        $post = get_post( $_REQUEST['post'] );
    } elseif ( isset( $_REQUEST['post_id'] ) ) {
        // wp-admin/async-upload.php
        $post = get_post( $_REQUEST['post_id'] );
    } else {
        return $upload;
    }

    if ( ! $post || empty( $post->ID ) ) {
        return $upload;
    }

    $taxonomy = 'category';

    // Get the terms associated with the post
    $terms = get_the_terms( $post->ID, $taxonomy );

    if ( $terms && ! is_wp_error( $terms ) ) {
        // Use the first term found
        // Posts should only have one category assigned
        $term = array_shift( $terms );

        // Add the taxonomy name to the uploads path
        $upload['path'] = path_join( $upload['path'], $term->slug );
        $upload['url']  = path_join( $upload['url'], $term->slug );
    }

    return $upload;
}

add_filter( 'upload_dir', 'add_taxonomy_to_upload_dir' );