You're using an article to poskin the Halacha? Obviously everyone can do whatever they want, but this article looks to be one of those articles that appears this time every year in mass market newspapers about Passover. And the woman it's about doesn't appear to be claiming to be observant in any major way.
While I've never heard anything about star anise for Passover, I know that cardamom is on many lists of impermissible things for Ashkenazim, and since that is listed in a recipe there, I'd certainly be wary if you are trying to be strict in any way.
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