drainer: fix codec race condition in integration test (#16845)

msgpackrpc codec handles are specific to a connection and cannot be shared
between goroutines; this can cause corrupted decoding. Fix the drainer
integration test so that we create separate codecs for the goroutines that the
test helper spins up to simulate client updates.

This changeset also refactors the drainer integration test to bring it up to
current idioms and library usages, make assertions more clear, and reduce
duplication.