Why do some login pages force the user to entire their username/email first, and then the password?

I am not an UI/UX designer. I am just a frequent Amazon user.

For some time now Amazon appears to have been changing its login page. About half the time I would get a run-of-the-mill (what I call a "single-step") login page, with email and password textboxes. The other half the time, however, I would be greeted by only the email textbox.

After I enter my email, the page reloads, now displaying a "Hello, [name]", and then followed by the password textbox.

I use Amazon as an example because it is the site I use the most frequently that has a login page (aside from my email). Another example would be Gmail, which used this two-step login page until I stopped using it.

Why do some login pages use this two-step login page, as in they force the user to entire their username/email first, and then the password?

Faster access or improved error messages? I thought maybe the website would query its databases for the email entered on the first page, and the load the second (password) page only when a corresponding email has been found. But a simple "no account found with that email address" message works equally well with either system (single- or two-step login), and this is what Amazon does whenever I do get a single-step login page. For me, the much longer two-step login page is what made me stop using Gmail in the first place.