How to extract heavily corroded anode rod?
If its corroded and enlarged all the way to the bottom you may have to cut it loose. In the tank it will continue being dissolved by the minerals until there's nothing left. And while that's happening the new rod will be in place.
You can try wrenching it out and probably break off chunk's of anode. This also shouldn't be an issue unless you plan on flushing the tank in which case there may be debris blocking the port. But these pieces will eventually dissolve. too.