Yes, this is gluten free
Single spices and herbs are gluten-free. Asafoetida is the one exception in this group — it is commonly cut with wheat flour as an anti-caking agent, so buy it labeled gluten-free. Pre-mixed blends are also worth checking for flour carriers.
star anise is covered by CiCi's entry on single spices and herbs, which share this answer and the reasoning behind it.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.