@Dominika34 No, absolutely not.
If you attempt to stay beyond the end date of your registered booking, you would be trespassing on the host's property. Since your request to change the checkout date has been confirmed, you are required to vacate the home on that date.
As a 3-month booking, any partial refund you receive for shortening the stay would be subject to the Long-Term Reservation Policy ,which you agreed to at the time of booking. This policy requires you to give 30 days notice for refunds of unused nights - any additional refund is solely at the host's discretion. You don't get to squat at the property after your checkout date just because you feel you deserved more of your money back.
Some hosts are amenable to refunding guests for dates that they are able to successfully re-book, so you could try to ask about that, but if you try to overstay after your new checkout date you will be charged a penalty fee and possibly banned from Airbnb.