◇ Could this help me?
Yes. The underlying claim is correct and the mechanism is easy to verify for yourself: a directly connected tool puts its whole response into context with no filter, while a script decides what crosses that boundary, and on tool calls that return large payloads the difference is the single biggest context saving available. The published vendor guidance on executing code against tool servers says substantially the same thing, so this is not one creator's theory. General practice, with two honest notes: the gain is small for tools that return little, and the convenience version of this is a third-party skill that deserves the same scrutiny as any other installed code, while the pattern itself can be implemented without installing anything at all.
I want to stop injecting whole tool responses into my context window. Take the tool servers I currently have connected, and for each one tell me how large a typical response body is and how much of it I actually use. Then, for the two worst offenders, write me a script that performs the same operation and returns only the fields I need, with the filtering done in the script rather than by you after the fact. Show me the script before running it, explain what credentials or access it requires, and tell me honestly which of my connected tools are small enough that converting them is not worth the effort.