To add on to LeninWeave’s great comment, Lenin would also take down Kautsky even in works not focused on him. Kautsky and Kautskyites, Kautskyism, etc are mentioned 89 times in The State and Revolution, such as here:

In this remarkable argument, Marxism takes a tremendous step forward compared with the Communist Manifesto. In the latter, the question of the state is still treated in an extremely abstract manner, in the most general terms and expressions. In the above-quoted passage, the question is treated in a concrete manner, and the conclusion is extremely precise, definite, practical and palpable: all previous revolutions perfected the state machine, whereas it must be broken, smashed.

This conclusion is the chief and fundamental point in the Marxist theory of the state. And it is precisely this fundamental point which has been completely ignored by the dominant official Social-Democratic parties and, indeed, distorted (as we shall see later) by the foremost theoretician of the Second International, Karl Kautsky.

Part of what makes Lenin so fun to read is that he never shies away from taking down those that drag the movement down.