It's more accurate to say that "bank depositors" are taking the hit, in the form of increased FDIC fees. Which end up reflected in lower interest rates for bank savings accounts. If you only keep a negligible money in bank accounts, then you aren't paying for this.
If you are keeping a lot of money in the bank, then yes, you are paying for this. But you are also gaining, in a sense, from the stability of the banking system.
This is also assuming that the sale of SVB's assets doesn't end up covering the full cost, and that the remaining cost is large enough to result in a meaningfully sized special assessment on FDIC member banks. My understanding is that neither of these outcomes are a given or even likelier than not.
If you are keeping a lot of money in the bank, then yes, you are paying for this. But you are also gaining, in a sense, from the stability of the banking system.