[lib] Get rid of effect in useUpdateRelationships

Summary:
Kamil's work in D13486 lets us greatly simplify this code.

Depends on D13489

Test Plan:
I tested with two devices: one iOS simulator, one physical Android. I followed the steps below twice, with iOS / Android alternating roles:

1. User A and user B create accounts
2. User B backgrounds the app
3. User A searches for user B and sends them a friend request
4. Confirm notifs are received. Confirm chat shows up as DM in UI
5. User A backgrounds the app
6. User B accepts the friend request
7. Confirm notifs received

Reviewers: kamil

Reviewed By: kamil

Subscribers: tomek

Differential Revision: https://phab.comm.dev/D13496