[lib] Make update-handler keyserver-specific

Summary:
One quick change - getting the connection status of the correct keyserver.

https://linear.app/comm/issue/ENG-5781/update-updatehandler

Depends on D11092

Test Plan: Generate an update on the server and check if it gets dispatched and acknowledged.

Reviewers: inka, kamil, michal, atul

Reviewed By: inka

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D11094