Cooking is a bit difficult. Most Embassies want to see a real cooking class... something that goes over months or even longer. And these courses are costly...
On their website is nothing mentioned that one has to be a resident... so... it should be "no problem". Just to make it sure you should contact them...
Since you can't be on two active visa at the same time, your ED Visa should be automatically been canceled already at the moment they stamped you in with DTV.
"not enough, qualified, correct, refused" What now? Makes no sense, somehow.
I too wonder how long this cooking course is? 2 days for Pad Thai and Som Tam? Well... at other places people get a DTV for an dentist appointment... but...
Something doesn't match... they don't refuse without valid reason. They can, that's correct, but that doesn't happen. Same as the IO at arrival... he can deny entry, even if you have a valid visa, but also that is just the theorie.
You say that your cooking class is qualified, the Embassy say that this is correct, but at the same time they reject your application and they want to give you an ED-Visa instead? Doesn't make sense somehow... some small detail is probably missing here...🙄🤔