4000zl net which I'm not sure is enough to live off
It's about the median wage in Warsaw in total, out of which people pay for accommodation, bills etc. After expenses, you won't be rich but you won't be poor either.
Not sure if you have a car, but you may not need it to save on the costs.
In Warsaw, nobody needs one since the public transport is excellent. I agree with you, the OP should go for it.