Wp custom post custom capability not working together

I am trying to make a custom post type editable by a group of people (i.e. The users' department) instead of only the author. I don't want to let them edit posts created by people of other groups(department). I am using the map_meta_cap filter to map the custom capabilities to solve this issue. Which is actually working fine. If I check it like: user_can( $user_id_of_who_is_editing, 'edit_post', $post_id ) It returns true for users of same department.

Now, if the non-owner user, who belongs to the same department, this error shows up:

You are not allowed to edit this post.

If wordpress does not check current_user_can( 'edit_post', $post_id ), how does it check and how can I bypass it?

Map metacap filter:

add_filter( 'map_meta_cap', function( $caps, $cap, $user_id, $args ) {
    global $dept_based_cap_post_types;
    
    if( isset( $args[0] ) ){
        $post = get_post( $args[0] );
        if( isset( $post-post_type )  in_array( $post-post_type, $dept_based_cap_post_types ) ){
            $edit   = edit_$post-post_type;
            $delete = delete_$post-post_type;
            $read   = read_$post-post_type;
            
            $post_belongs_to_users_department = lu_post_under_users_dept( $user_id, $post-ID );
        }
        else {
            return $caps;
        }
    }
    else {
        return $caps;
    }

    /* If editing, deleting, or reading a post, get the post and post type object. */
    if ( $edit == $cap || $delete == $cap || $read == $cap ) {
        $post_type = get_post_type_object( $post-post_type );

        /* Set an empty array for the caps. */
        $caps = array();
    }

    /* If editing a post, assign the required capability. */
    if ( $edit == $cap ) {
        if ( $post_belongs_to_users_department || ( $user_id == $post-post_author  'draft' == $post-post_status ) )
            $caps[] = $post_type-cap-edit_posts;
        else
            $caps[] = $post_type-cap-edit_others_posts;
    }

    /* If deleting a post, assign the required capability. */
    elseif ( $delete == $cap ) {
        if ( $post_belongs_to_users_department || ( $user_id == $post-post_author  'draft' == $post-post_status ) )
            $caps[] = $post_type-cap-delete_posts;
        else
            $caps[] = $post_type-cap-delete_others_posts;
    }

    /* If reading a private post, assign the required capability. */
    elseif ( $read == $cap ) {

        if ( 'private' != $post-post_status )
            $caps[] = 'read';
        elseif ( $post_belongs_to_users_department || ( $user_id == $post-post_author  'draft' == $post-post_status ) )
            $caps[] = 'read';
        else
            $caps[] = $post_type-cap-read_private_posts;
    }
        
    return $caps;
}, 10, 4 );

Code for custom post type registration:

$capabilities = array(
    'edit_post'           = 'edit_registration',
    'read_post'           = 'read_registration',
    'delete_post'         = 'delete_registration',
    'delete_posts'        = 'delete_registrations',
    'delete_others_posts' = 'delete_others_registrations',
    'edit_posts'          = 'edit_registrations',
    'edit_others_posts'   = 'edit_others_registrations',
    'publish_posts'       = 'publish_registrations',
    'read_private_posts'  = 'read_private_registrations'
);

$args = array(
    'labels'             = $labels,
    'public'             = false,
    'publicly_queryable' = false,
    'show_ui'            = current_user_can( 'edit_programs' ) ? 'edit.php?post_type=program' : true,
    'query_var'          = false,
    'capabilities'       = $capabilities,
    'has_archive'        = false,
    'hierarchical'       = false,
    'menu_icon'          = 'dashicons-clipboard',
    'supports'           = array( null ) // Array must contain a value to remove the default fields
);

register_post_type( 'registration', $args );