I don't know if they're a wholesaler (or if that even matters) but the tax is collected by the distributor. So when Costco buys it, they pay the tax.
Sweetened beverage tax
Beginning Jan. 1, 2018, the City of Seattle will impose a sweetened beverage tax. View
Ordinance 125324.
The sweetened beverage tax is a tax on the distribution of sweetened beverages in the city of Seattle. The tax is collected on the final distribution of sweetened beverages by a distributor. The tax is not collected by the retailer nor is the tax burden intended to fall onto the consumer. The intent of the sweetened beverage tax is to tax the distributions of sweetened beverages into Seattle for retail sale in Seattle.
Sweetened beverage tax - Business License Tax | seattle.gov