[lib] Handle private threads differently from personal ones in thread list search

Summary:
The parent diff adds private threads to the results, but they show up as personal threads.

This diff makes them show up correctly.

Depends on D13537

Test Plan: In combination with the rest of the stack, test creating a PRIVATE thread via thread list search on both web and native

Reviewers: tomek, kamil, inka

Reviewed By: tomek

Differential Revision: https://phab.comm.dev/D13538