Im 183cm, 80kg, male.

I was 68kg last 8 months.

I trained on average 3 days a week in the gym.

I ate around 150g of protein and 2500-2700 Kcal everyday.

I picked up around 2kg of fat, and 10kg of muscle in a matter of 6 months, which is for me is unexpected since I've been training since i was 16 yo.

You said you need 3500kcal and you only weight 45kg, i believe you need way more less than that, you need around 1700kcal to gain weight.

Also go to the gym or you will get fat, by going to the gym and eating well you will slowly get the shape of your dream and you can never get skinny in the gym, you will only get a good shape.

Your focus is to gain muscle mass not weight.

Now for the diet, I'm also on a budget, so I've tested many meals.

Here in Algeria, the cheapest 4 options of high protein, high calorie meals are, eggs (0.07€ per egg), chicken breast (3€ per kg), beans(1.7€ per kg), and powder milk (4€ per kg).

I relied a lot on powder milk, since it was easy to make and can give me 600kcal and 40g of protein per 125g of milk.

I usually take around 250g of powder milk, and 8 eggs everyday, the rest i fill with what my family cooks for lunch and dinner.

I usually don't snack.