John has since moved on and is earning more at ABC Corp instead. XYZ Corp has duly reclaimed John's old email address, and John cannot receive emails at said address any longer.
This is the situation the OP is in. It was never a "fake email address". They did not literally type "first.last@org", that was an example suitable for using in their comment.
[edit: I'm actually wrong with that last statement, as it turns out. While it wasn't a fake email address, the situation is slightly more nuanced in that OP actually did say "{first}.{last}@hhi.fraunhofer.de" in the paper, as there were multiple authors who all had the same email address format - see https://news.ycombinator.com/item?id=41479618. I still think this is a valid method, though, and it's certainly not fake. Besides, the problem I outlined sounds like it probably remains an issue even if it's not the exact problem OP is experiencing.]
In our case it's for saving space in the paper, and also for reducing spam. This small change may now seem silly in the age of LLMs, but the papers that have full email addresses in them get a considerable amount of fake conference and journal participation emails, which is annoying.
I still think this is valid (and certainly not the fake email address that people are calling it), but yeah, it's not what I thought it was.