[lib] Extract hook to send logout message to primary device

Summary:
Part of ENG-9710.
We want to send this message not only on secondary device logout, but also on legacy logout when use_new_flow is received

Depends on D14032

Test Plan: Performed secondary device logout. Confirmed that primary device received the message.

Reviewers: kamil, varun

Reviewed By: kamil

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D14033