[desktop] Stop checking for a new version after download

Summary:
This was the source of the issue ENG-3311, more information in the comments.
The short version is that if we checked for updates (and didn't find any) after downloading a new desktop version an error would appear when user tried to quit and update.

Test Plan: Check if the error stops happening.

Reviewers: tomek, kamil, ashoat

Reviewed By: ashoat

Subscribers: ashoat, atul

Differential Revision: https://phab.comm.dev/D7095