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Hi! It should have the same number of sigma and pi bonds regardless of whether or not the molecule has resonance. Otherwise the structures would not be equal. Because SO3-2 has two single bonds and one double bond, here are three sigma bonds (one per single bond and one in the double bond) and one pi bond (one from the double bond).
I believe Sigma and Pie bonds aren't meant to describe the actual thing, such as resonance being an average of the bond lengths, but instead describing how we describe bonded molecules as single, double, triple bonds.
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