[net processing] Move send ping message logic into function

Summary:
Partial backport of core#20721:
https://github.com/bitcoin/bitcoin/pull/20721/commits/0b43b81f69ff13dbc1e893a80950f186690b4f62

Ref T1696.

Depends on D10875.

Test Plan:

ninja all check-all

Reviewers: #bitcoin_abc, PiRK

Reviewed By: #bitcoin_abc, PiRK

Maniphest Tasks: T1696

Differential Revision: https://reviews.bitcoinabc.org/D10876