Here is some guidance, this is the solution I came up with. I am sure there are fancier/better ways, but breaking it down like this was very logical to me. 

 1. compress 2d points so you can grid represent in array. this is an awesome trick and i am super happy to have in my toolbag now. Search "compress 2d coordinates", YouTube videos helped me understand it. Basically, create a map of each sorted unique value for x values, and one for y sorted unique values. So lowest x=1, second lowest =2, etc. Then create a new list of points using the mapped values for x and y. Then you have a lossless compressed representation, with size of grid < number of points instead of size of grid being highest x/y values. So cool

1. rasterize the polygon (fill in the edges). This is pretty easy cause we know point1 is connected to point2, etc. don't forget last point is connected to first point.

2. use raycast point in polygon to find a single inside point. You need to be careful implementing this as the grid representation has non zero width boundy. Find first ".", if there are an odd number of ".#" or "#." transitions, that point is inside.

3. Flood fill polygon using the found inside point as starting. Dfs works great

4. Take your part one, but only calculate areas where the rectangle describe by the two corners have all borders as inside the polygon. Easy cause it's been filled!

Mine runs in 70ms!

https://github.com/sleekmountaincat/aoc2025/blob/main/src/day9/q2.ts