Authorization code is rejected with "Incorrect password" and old account email address appears

[data-sync-user]

Originally reported via Slack:

https://mozilla.slack.com/archives/C4D36CAJW/p1646162658251209

!Screen Recording 2022-03-07 at 22.52.09.mov|width=1200,height=1548!

1. I have a personal Firefox Account with mozilla@(redacted).de as my primary and caugner@(redacted).de as my secondary email address. (Note: Originally, I created that account with firefox-sync-beta@(redacted).de as primary address.)
2. When I login with my primary email address and my current password, I get an “Account authorization code” to both email addresses. (Note: Sometimes my current password gets rejected instead, even though I always auto-fill it from the Firefox password manager.)
3. However, when I submit that authorization code, I always get an “Incorrect password” error message and my old email address shows up.
4. Therefore I’m unable to login to my Firefox Account on my new device (Mac OS, Firefox 97.0.1).

┆Issue is synchronized with this Jira Bug
┆Attachments: Screen Recording 2022-03-07 at 22.52.09.mov

[data-sync-user]

➤ Claas commented:

Reopening, as the issue persists for me despite #12451 ( https://github.com/mozilla/fxa/pull/12451|smart-link ) having landed.