How to reference only affected rows in AFTER UPDATE trigger
Use the inserted table, which is a special table available inside triggers containing the rows that will be updated/inserted into the table.

ALTER TRIGGER tr_app_bread_crumbs_afterupdate
ON [dbo].[app_bread_crumbs]
AFTER UPDATE
AS
BEGIN 
    UPDATE [dbo].[app_bread_crumbs]
    SET last_updated_by = SYSTEM_USER,
    last_updated_on = GETDATE()
    FROM dbo.app_bread_crumbs abc
    WHERE EXISTS (SELECT 1 FROM inserted i WHERE i.id = abc.id);
END