Comment: comments are left as wrong account if multiple Google login is used in same browser

[worldomonation]

Steps to reproduce the behavior

Prereq. Create/own two Google Login-based WP accounts.

1. Go to https://wordpress.com/log-in.
2. Log in to WordPress.com using Google Account 1.
3. Once login is complete, log out.
4. Return to https://wordpress.com/log-in.
5. Log in to WordPress.com using Google Account 2.
6. Once login is complete, go to a site with comments enabled.
7. Click on a post
8. Scroll down to the Comment section and click on the comment box.

What I expected to happen

#comment-form-identity folds out with the gravatar and display name of Google Account 2.

What actually happened

#comment-form-identity folds out with the gravatar and display name of Google Account 1.

Context

User testing.

Browser / OS version

OS: macOS Big Sur 11.1 (20C69)
Version 88.0.4324.150 (Official Build) (arm64)
Browser: Safari Version 14.0.2 (16610.3.7.1.9)
Browser: Firefox Nightly 87.0a1

Is this specific to the applied theme? Which one?

No.

Does this happen on simple or atomic sites or both?

Simple only.

Is there any console output or error text?

No.

Level of impact (Does it block purchases? Does it affect more than just one site?)

Moderate - user may inadvertently leave comments as the Google Account 1 when they meant to use another account.

Reproducibility (Consistent, Intermittent) Leave empty for consistent.

Consistent.

Screenshot / Video: If applicable, add screenshots to help explain your problem.

It's a bit long and I'm juggling multiple windows, but illustrates the issue.
https://user-images.githubusercontent.com/6549265/107707504-d2973e00-6c76-11eb-898a-c72d78e4d83a.mov

Screenshot of the new comment notification email:

[github-actions]

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