Another option is to talk to someone with a milling machine, or a big drill press/pillar drill. Do NOT try this with a hand drill
If you treat this as a bolt broken off in a hole, then the process is similar.
You'd start by fixturing the bike frame under the drill/mill spindle such that the seat tube is vertical and centered. Then you have to secure the frame against moving or spinning. This step often takes longer than the drilling
If the hole in the tube is 16mm then start with a 16mm demming twist bit and it should align well with the hole. Adjust if required. Use plenty of WD40 or a specific aluminium-cutting lubricant to protect the drill.
Then step up through 18mm, 20mm, and maybe 21mm. Either the force of the drill will overcome the corrosion and the post will move on the drill, or you'll bore out enough of the wall thickness so what's left will invert itself by poking a thin screwdriver down the sides between frame and remaining seatpost. There is a risk the stub of seatpost falls down inside the frame, which is to be avoided.
Ideally you want to avoid cutting any of the steel from the frame, but a light touch won't make any real difference. The frame will be narrowest in the top 100mm, and will be slightly wider internal diameter below that point.
When installing a new seat post, clean remaining corrosion from the bore with a wiffle stick or a light cylinder hone. Use grease or an assembly lube to keep the steel off the aluminium seatpost, or fit another metal. Anodised aluminium seat posts may be perfect for this task.