net_processing: make more of PeerManager private
Summary:
Partial backport of core#20811:
https://github.com/bitcoin/bitcoin/pull/20811/commits/0df3d3fd6bbbd0e06116797177ba797580553250
Ref T1696.
Test Plan:
ninja all check-all ninja bitcoin-fuzzers
Reviewers: #bitcoin_abc, PiRK
Reviewed By: #bitcoin_abc, PiRK
Maniphest Tasks: T1696
Differential Revision: https://reviews.bitcoinabc.org/D10886