test: Combine sync_send_with_ping and sync_with_ping

Summary:
This reduces bloat, complexity, and makes tests less fragile to intermittent failures.

This is a backport of core#28409

Note: I don't know if this already fixes any existing intermittent failure, but at least it will prevent introducing a new one when backporting core#27675

Test Plan: ninja check-functional

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D15979