I think the noun phrase and wiki link you're looking for is "door-in-the-face technique", https://en.wikipedia.org/wiki/Door-in-the-face_technique.
Thanks!
Edit: Specifically, reading through https://en.wikipedia.org/wiki/Negotiation#Tactics, I believe both the "Highball/Low-ball or Ambit claim" and "Anchoring" sections describe the phenomena I was thinking of.
I also found that vaguely explaining to GPT-4 the description you start with, also produced the proper names for me. Unstructured querying that I could not Google-Fu