Wp-calypso: Jetpack connect: Connect from site banner fails

[sirreal]

When connecting a new Jetpack user to a site via wp-admin banner, connection fails or ends in incoherent state.

To reproduce

1. You must have a connected Jetpack site.
2. Add and invite a new user to the site via wp-admin.
3. Accept invite and log in the site with this new user. Do not log in using WordPress.com credentials.
4. Ensure you are logged in to WordPress.com with a different user who is _not_ currently connected to the site.
5. Visit the Jetpack Dashboard, you should see a banner nudging you to link. Click "Link to WordPress.com".
   
6. There seem to be two unsatisfactory outcomes.

What I expected

Follow a Jetpack connection flow and be returned to a site dashboard, either in Calypso or wp-admin.

What happened

There were two outcomes.

Initial attempt

Here, we're immediately presented with a "Return to site" button. Click it and we return to the site without connecting. Note this gif loops, but there are _two_ attempts here. You can see in the second attempt that "Approve" appears.

It seems that some of the state may not be loaded which is causing a "Return to site" button to be shown rather than the desired "Approve" button.

Subsequent attempts

If you do see "Approve" and click it, the site is connected. However the return to a connect form with a "Finishing set up…" notification. What to do, there's not obvious way ouy?

Back at the site, you _are_ connected at this point.

Observations

There appear to be two main issues.

1. The user is shown a button to return without connecting.
2. If they wait and see the "Approve" button, the user is connected but arrives at a dead end.

Reported by @keoshi here: p1498748549590798-slack-jpop-design

[sirreal]

When I created this issue I was able to reproduce consistently. Later I attempted to reproduce again with a different site and was unable.

[zinigor]

cc @roccotripaldi who's working on the problem. I'm going to close the Jetpack issue, because it's not a Jetpack issue. Thanks!