[avalanche] Convert the multi_block_register test to use the context

Summary:
This is a follow-up to D10261.

Ref T1854.

Depends on D10261.

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/D10262