net: Avoid redundant and confusing FAILED log

Summary:

Remove a redundant and confusing "FAILED" log message and gets rid of
the unused return type in ProcessMessage

Backport of core PR19293.

Depends on D4150.

Test Plan:

ninja all check-all

Reviewers: #bitcoin_abc, majcosta

Reviewed By: #bitcoin_abc, majcosta

Subscribers: majcosta

Differential Revision: https://reviews.bitcoinabc.org/D8777