It really depends on what kind of Asian food you like making. I have a ton of seasonings too, but I tend to skip Thai. We have a great Thai place so I feel less need to make that myself.
For Japanese food, the unusual-for-the-US seasonings are soy sauce, rice vinegar, konbu, bonito flakes, sake, mirin, miso, and maybe sesame oil. That’s really all you need to make almost every kind of simple Japanese food. Add nori and wakame if you want to make rolled sushi and miso soup with seaweed, respectively. I keep almost all of that on hand because I love Japanese food. You can get by without mirin; substitute more sake and add some sugar to make up the sweetness.
Chinese can get pretty wild with ingredients (daylily buds anyone?) but you can do a lot with just soy sauce, hoisin sauce, fermented black bean sauce, and sesame oil. I usually substitute black rice vinegar with regular rice vinegar and a splash of balsamic and soy sauce, and use sake in place of whatever Chinese rice wine they call for. Edited to add: how I forgot Szechuan peppercorns I’ll never know, and you can live without them, but why? They are so distinctive and soooo good.
Korean I can’t help you with! XD I like kimchi but very rarely cook Korean-specific food aside from DIY not-really-but-we’ll-pretend-they-are banh mi sandwiches. Same deal with Vietnamese — I rarely cook that either.
Indian … Indian is a long hot delicious mess of spices. It’s so worth it but s o much pantry space. Cumin, coriander, turmeric, black mustard seeds, and garam masala will go a long way though, along with (I consider these normal pantry staples but maybe not everyone does?) cinnamon, ginger, cloves, and cayenne.
(Also, I have derailed the chat. I apologize. I was just so excited to talk spices. ^^; )