The key point is: your plastic savings mainly affect your own garbage volume and local infrastructure, not what's happening in Asia. Those are two completely different problems. When you use less plastic, you produce less waste that your city has to process - that has a direct effect. But yeah, it doesn't change the fact that garbage ends up in the ocean elsewhere.
The frustration is totally understandable. Only thing is: if everyone in Europe says "oh, China dumps everything anyway, why should I bother saving?", then even less happens. It's more that pressure on manufacturers and politicians builds up when consumers buy less and shop without packaging - that sends a signal. And honestly, there are still way too many unnecessary packages here too, the kind that just don't need to exist. Putting pressure on that makes sense, regardless of what's going on elsewhere.
If it's weighing on your conscience: maybe it helps to mentally separate this. Your plastic savings are worthwhile for *your* surroundings and conscience - not as a solution to global waste problems. And those global problems need different solutions (international agreements, better waste management there, etc.), which you as an individual can't really influence. That's not your fault and it's not frustrating when you look at it that way.