How do I play the original Warcraft 3 now?

One has to install the full update. This is because even without buying Reforged, the World Editor can show Reforged models.

If storage space is a concern consider investing in a 512 GB SSD to act as a gaming partition. These cost £50 for reputable ones from Samsung and possibly less from lower quality vendors. 512 GB SSD is more than enough space for a few games.

Try uninstalling the existing version. Then from the BattleNet application installing Reforged. I would imagine this as a work around as it is effectively re-installing Warcraft III.

Check there is not a new mac installer for Warcraft III. Otherwise if there is no native BattleNet application then you may want to consider making a topic about it.