transformer windings
You should use magnet wire like the wire you removed and like the primary only larger. Larger sizes are available in square wire. The primary will not demand much more current than the turns ratio multiplied by the secondary current.

You should probably remove the magnetic shunt bar(s) from the transformer. The function of the magnetic shunts is to limit the primary current if a short circuit occurs on the output of the transformer. They do something like adding series resistance. They cause the secondary voltage to drop as the load increases. Some MOT project descriptions recommend their removal.

There may also be an extra secondary winding for the filament of the megnetron tube. That can also be removed.

Adding about 12 turns to the primary winding will reduce the extra current in the primary and increase the transformer efficiency.

You should probably use the largest wire that will fit comfortably in the space available. Using larger wire than is necessary will reduce the transformer losses and make it run cooler. Microwave ovens that are designed for home use normally operate for only a few minutes at a time a few times a day. To minimize cost, the transformer is not designed to carry full current continuously. The primary winding will git hot if it carries full current continuously, but it may help reduce the overall temperature if the secondary wire is larger than it would normally need to be to carry the desired current. Another answer suggests parallel connection of smaller wire rather than large wire that may be difficult to wind. That is a good idea, but if you gain extra winding space by removing the magnetic shunts, the winding does not need to be as tight to fit.

If you search the internet for microwave oven transformer (MOT) projects, you will probably find lots of advice. It would be a good idea to look at various YouTube and text descriptions to learn as much as possible.