Bluetick1010

I think you got some of the ideas mixed up but you are spot on on the concept that higher risk requires higher spread to compensate for the added risk taken. But it is not really applicable on this equation.
When we say Z = OAS + Option Cost, we are not refering to Z spread from a option free bond vs the OAS from another bond with optionionality. The idea is simply that for an option free bond, the Z spread and its OAS is the same because there is no optionality (and option cost is zero). But for a bond with embedded option, the Z spread is higher than it’s OAS because Z spread reflects credit, liquidity and option risk. But OAS is already adjusted for option cost or you can treat it as option removed spread.
Thus, when we compare bond without embedded option with Z spread of 350 bps against a callable bond with embedded option with Z spread of 500 bps and OAS of 300 bps with the same duration, we use the OAS of 300 bps to compare against the option free bond 350 bps spread and not the Z spread of 500 bps. This allows us to make a more meaningful apple to apple comparison because we have already removed option risk from the callable bond by using OAS to compare against a option less bond’s Z spread (which is also same as it’s OAS).
Hope this clarifies your undestanding