Right.
So when removing the email address, Zammad is forced to also update the login name (because other wise you couldn’t e.g. add the same address to another user). When re-adding the email address to the affected user, the login name is already set (no matter if it’s the automatic one or one that you’ve chosen).
For this reason Zammad does not enforce an update on the login attribute when setting the email. This does work as designed. You can use both, login or email to login - it technically doesn’t matter.
You can learn more on the attributes on our documentation, it also hints you to further options on e.g. updating the login attribute if needed. Users — Zammad documentation