Resolves #92246

Proposed Changes

• Use the recognized_logins cookie to detect existing users and don't show them the CTA.
• Make sure the CTA is displayed only when the form responds with unknown_user. This fixes a bug where the CTA is displayed when an empty form is submitted and the calypso_login_block_login_form_get_auth_type_failure (error_code: unknown_user) experiment exposure event was fired previously.
• Update the experiment name.

Why are these changes being made?

• We want to re-run the previous experiment with a few updates. More context can be found here: pdxWSz-1yz-p2#comment-488

Testing Instructions

• In an incognito window, go to http://calypso.localhost:3000/log-in and enter a non-existing email.
• Verify that a "User does not exist." error is displayed.
• Close and re-open the page.
• Now manually assign yourself to the "Treatment" group of the 21864-explat-experiment following this guide: PCYsg-SwK-p2 (Manually assign with Abacus assignment bookmarklet). Check the video below to see how it works. Note that you may have to restart the incognito session if the bookmarklet doesn't work.
• After assigning yourself to the "Treatment" group, enter a non-existing email again.
• Verify that you see the "User does not exist." error and the migration notice.
• Verify that the migration notice CTA points to https://wordpress.com/move/.
• Manually add a recognized_logins cookie with some value to the calypso.localhost domain.
• Refresh the page, enter a non-existing email again, and make sure the CTA is not displayed.
• If you want to do a proper test for the recognized_logins cookie, setup your local Calypso to run on wordpress.com (where the cookie is set by the public api) following this guide: PCYsg-5YE-p2. Or change the domain where the cookie is set on your sandbox.

Pre-merge Checklist

• Has the general commit checklist been followed? (PCYsg-hS-p2)
• Have you written new tests for your changes?
• Have you tested the feature in Simple (P9HQHe-k8-p2), Atomic (P9HQHe-jW-p2), and self-hosted Jetpack sites (PCYsg-g6b-p2)?
• Have you checked for TypeScript, React or other console errors?
• Have you used memoizing on expensive computations? More info in Memoizing with create-selector and Using memoizing selectors and Our Approach to Data
• Have we added the "[Status] String Freeze" label as soon as any new strings were ready for translation (p4TIVU-5Jq-p2)?
• For changes affecting Jetpack: Have we added the "[Status] Needs Privacy Updates" label if this pull request changes what data or activity we track or use (p4TIVU-aUh-p2)?