Share Extension: Site picker takes too long to load for accounts with many sites

We received this feedback about the time it takes for the site picker to load in the share extension (internal ref: p1P4aZ-3N4-p2):

The last thing I noticed is that the mobile app’s fetching of the possible sites to publish to within the share extension flow consistently took 10-15 seconds. It would be awesome to have this cached more aggressively if possible.

I see a similar delay when I share to the app while logged in to my a8c account, and the delay occurs every time I open the share extension (not just the first time). It definitely feels like we need better caching there, especially because this blocks actions in the share extension — the first thing you see after selecting WordPress as the share target is that it's fetching your sites.

I also tested while logged in to an account that only has one site and another account with 18 sites, and it was very fast to load in both cases, so this is likely only a noticeable issue for accounts with many sites.

Tested on iPhone XS, iOS 12.1.4, WPiOS

Start by tracing the share extension's site-picker fetch and comparing load times for accounts with many sites. Verify the behavior when reopening the extension, then consider the work complete when repeated openings no longer block for 10–15 seconds for large accounts.