Rationale behind Q-learning

I am reading Sutton Barto on Reinforcement Learning. I understand that $$TD(\lambda)$$ methods propose better performance than Monte Carlo methods, with TD methods combining advantages of Dynamic Programming and Monte Carlo approaches.

The transition to Q-methods : SARSA, Q-Learning, Expected SARSA is unclear to me. Which gaps is filled by Q-methods, what is the rational behind their use rather than TD methods ?

There isn't really such a thing as "Q methods" in the sense that you are using it. All of SARSA, Q-learning and Expected SARSA are TD methods. Specifically they are using TD approach in the context of action values, which is necessary for value based model-free control problems, because if you just used state values $$V(s)$$ then you have no way to generate your best guess at the optimal policy. Using $$Q(s,a)$$ immediately gives you $$\pi(s) = \text{max}_a Q(s,a)$$.
Model-free Monte Carlo control likewise must use estimates of $$Q(s,a)$$ which is why there is not really a clear class of methods called "Q methods", although it is a matter of convention what all these things are called and they are all inter-related in any case.