Move NotifyNumConnectionsChanged logic to private method.

Summary: This is a partial backport of Core PR14335 : https://github.com/bitcoin/bitcoin/pull/14335/commits/edb5350c32cdf7f8487777b5cc1a2ebfcdfc9e75

Test Plan:

make check

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D4086