Each turn, each player can cast any number of artifact spells plus a maximum of one nonartifact spell.

Ethersworn Canonist takes into account spells that were cast earlier in the turn before Ethersworn Canonist entered the battlefield, including any spells that are somehow still on the stack. However, any spells on the stack as Ethersworn Canonist enters the battlefield have already been cast by that point, so they're not affected by it.