[Part 4] [tests] Add P2P interface to TestNode

Summary:
Partial backport of core PR11182 (commit 32ae82f)

Update the tests to the new P2P interface

Depends on D2326

Test Plan:

./test/functional/test_runner.py p2p-mempool p2p-timeouts

sendheaders

Reviewers: #bitcoin_abc, deadalnix, jasonbcox

Reviewed By: #bitcoin_abc, jasonbcox

Subscribers: jasonbcox, teamcity, schancel

Differential Revision: https://reviews.bitcoinabc.org/D2330