ahhh finally!!! It is the kitchen itself. I deleted only the whole kitchen room from the house (replacing counters, stove + fridge didn't help) and then my sim was able to cook normally using the same type of counters, stove and fridge. I still have no clue why but this kitchen just broke. I have yet to test if I can upload the house to gallery and place it from there and still have it function or will I have to fix the house manually... It's a house built by Harrie and deleting and then putting all the detail back in manually would be quite a hassle. :D
But thank you @crinrict for the suggestions (and just general moral support haha), it lead me to at least figure out how to get out of this pit even though the root cause still remains a mystery. :D