[backport#18247] test: Remove redundant sync_with_ping after add_p2p_connection

Summary:
Also replace the two-line (send_message + sync_with_ping) with the one-line send_and_ping

https://github.com/bitcoin/bitcoin/pull/18247/commits/faf1d047313e71658fb31f6b94fdd5d37705ab85

Depends on D6384

Concludes backport of Core PR18247

Test Plan:

./test/functional/test_runner.py

Reviewers: #bitcoin_abc, deadalnix, jasonbcox

Reviewed By: #bitcoin_abc, deadalnix, jasonbcox

Differential Revision: https://reviews.bitcoinabc.org/D6432