Protect: Math "Fallback" doesn't keep the username/password

This report is a partial upstreaming of this WordPress.org Meta ticket, as the situation applies to the WordPress.org login system: https://meta.trac.wordpress.org/ticket/4989

According to #2097 this may be intentional, but it's a bad user experience.

#### Steps to reproduce the issue

1. Get your IP blocked by the Protect API, or falsify the API response to pretend to be blocked.
2. Login and be faced with the Protect Math Fallback
3. Solve the Math problem correctly
4. Be redirected to the login page, with errors of: `Error: The username field is empty. Error: The password field is empty.`

#### What I expected
At step 4, I'd expect either:
a) The login details to be kept, and login attempted
or
b) The login user to to be recalled, and redirected to the login form with it filled in.
and
c) The error message shown to prompt the user to login again, rather than core thinking the details weren't submitted.

**Screenshots**
Example of step 4.