I think you're confusing two different axes. There is a difference between the cache state and the context state.
Imagine a conversation with turns X, Y, and Z. When the LLM "reasons" about the next token A it does: P(A | X,Y,Z) and then P(B | X,Y,Z,A), etc. It will eventually produce a result P(D | X,Y,Z,A,B,C). Instead of continuing the context from X,Y,Z,A,B,C it continues it from X,Y,Z so you have P(N | X,Y,Z,D). This is what is meant by dropping the reasoning. This is done to save cache context for the session.
This is a different thing than preserving the K/V state of P(N | X,Y,Z,D).
Imagine a conversation with turns X, Y, and Z. When the LLM "reasons" about the next token A it does: P(A | X,Y,Z) and then P(B | X,Y,Z,A), etc. It will eventually produce a result P(D | X,Y,Z,A,B,C). Instead of continuing the context from X,Y,Z,A,B,C it continues it from X,Y,Z so you have P(N | X,Y,Z,D). This is what is meant by dropping the reasoning. This is done to save cache context for the session.
This is a different thing than preserving the K/V state of P(N | X,Y,Z,D).