[identity] [7/n] Replaces sending messages with send_message function

Summary:
This utilizes the send_message function introduced in D10847 to reduce code duplication with sending messages through SplitSink

Depends on D10847

Test Plan: tested locally

Reviewers: varun, bartek

Reviewed By: bartek

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D10874