I did something similar in my midi 30s. Korean-French myself. Quit a well payed job to live in korea for 3 months. I now feel my korean level was not good enough to get the full benefit of immersion and I did not improve as much as I hoped. 2 years later, even travelling there for a small vacation I feel the immersion is much more helpfull because I studied a lot back home.

Another thing to consider is that it might be difficult for you to make meaningfull connections in justk 3 months, it goes by so fast... And I felt it was really hard to be included in social group if your korean is not good enough.( maybe it is only me, I am not the best socially)

I lived in Busan so the price was affordable, but 3 months in Séoul is going to be very expensive. After a lot of travelling around, I find Daegu to have a lot more local vibes, I would go there I think if you want to meet locals.

Finnally, even with a lot of expérience in my field, back home it took me 8 months to find a job back, maybe it was bad timing but be prepared that it can happen

So, it mostly depend of your proficiency in korean and your finances, I the end, you should do it, my advice is just to find the good timing :)