Is the manager considered responsible for cutting off employees' livelihoods when they are laid off due to company restructuring aimed at cutting costs, and is his failure to do so considered a betrayal of trust in his work?

If you perform your work completely, there is no sin upon you if the management dispenses with some employees, and your knowledge is not an injustice to them. The important thing is that you do not wrong anyone by describing them with what they are not, and that you do not wrong your management, or fall short in your work by concealing facts.