Different possible Lewis structures of peroxymonosulfate anion
So shouldn't the one that satisfies the octet rule be favored over the one with an extended octet?


That's only true when you are comparing resonance structures. Resonance structures only involve movement of electrons and not atoms.

It's not true for different Lewis structures, which are the ones you drew. There are lots of compounds which are perfectly stable but do not (in principle) satisfy the octet rule.

I would have mentioned the extreme instability of your multiple $\ce{O-O}$ single bonds in your alternative proposed structure, but the other answer beat me to it.