[avalanche] Convert the poll_and_response test to use context

Summary:
Similar to D10262, depends on D10262 and D10268.

Ref T1854.

Test Plan:

ninja check-avalanche-processor_tests

Reviewers: #bitcoin_abc, PiRK

Reviewed By: #bitcoin_abc, PiRK

Maniphest Tasks: T1854

Differential Revision: https://reviews.bitcoinabc.org/D10270