WordPress hook after post content and meta update

save_post and new_to_publish is enough, with some checks, to update post metadata. And you don’t need the redirection.

<?php
/**
 * Update Postmeta.
 *
 * @param integer $post_id Post ID.
 */
function wpse355298_job_publish_status( $post_id ) {
    // Check autosave.
    if ( wp_is_post_autosave( $post_id ) ) {
        return $post_id;
    }

    // Check post revision.
    if ( wp_is_post_revision( $post_id ) ) {
        return $post_id;
    }

    // Check permissions.
    if ( 'post' === $_POST['post_type'] ) {
        if ( ! current_user_can( 'edit_post', $post_id ) ) {
            return $post_id;
        }
    }

    $job_published_date = get_the_time( 'Y-m-d', $post_id );
    $expire_date        = date( 'Y-m-d', strtotime( $job_published_date. ' + 60 days' ) );

    update_post_meta( $post_id, '_job_expires', $expire_date );
}

add_action( 'save_post', 'wpse355298_job_publish_status' );
add_action( 'new_to_publish', 'wpse355298_job_publish_status' );