Programmatically allow a non-author to edit a post based custom meta field

Looking at current_user_can()‘s documentation, I see that it uses WP_User::has_cap(). So if your code (or the WP core code) uses something like current_user_can( 'edit_post', $post->ID ) to determine if the current user can edit the current post, you can use the user_has_cap filter (called in WP_User::has_cap()):

add_filter( 'user_has_cap', 'wpse360937_allow_manager', 10, 4 );
function wpse360937_allow_manager( $allcaps, $caps, $args, $user ) {
    // Bail out if we're not asking about a post:
    if ( 'edit_post' != $args[0] ) {
        return $allcaps;
    }
    // Bail out for users who can already edit others posts:
    if ( $allcaps['edit_others_posts'] ) {
        return $allcaps;
    }
    // Bail out if the user is the post author:
    if ( $args[1] == $post->post_author ) {
        return $allcaps;
    }
    $post_id = $args[2]; 
    $manager_id = get_post_meta( $post_id, 'manager', true );
    // Assumes the meta field is called "manager" 
    // and contains the User ID of the manager.
    if ( $manager_id == $user->ID ) {
        $allcaps[ $caps[0] ] = true;
    }
    return $allcaps;
}

(Code partly based on the User Contributed Notes on the user_has_cap filter docs.)