A little tough to see whats what, but welding what's there is going to work even if you did join it or cut it clean and butt something you will have to ream the seat pin again and it will probably last a short time. It looks like the seat tube passes throught the top tube. You could slip another tube internally butting it and use a smaller diameter post but the best thing is to replace the entire seat tube going oversize to make up for material lost getting the old tube out. Good luck.