[avalanche] Use the remote proof status to confirm the presence/absence of a proof

Summary:
This prevents a node from being out of sync from the network if it is missing the connection with a node.

Depends on D14664.

Test Plan:

ninja all check-all

Reviewers: #bitcoin_abc, PiRK, bytesofman

Reviewed By: #bitcoin_abc, PiRK, bytesofman

Subscribers: PiRK

Differential Revision: https://reviews.bitcoinabc.org/D14665