I would stick with the 15W oil on spring side. The single grade viscosity (there's not two viscosity numbers like 10W30, a multi-grade oil) will remain at a consistent viscosity during use and the relatively mild heat build-up from a working suspension. The consistent viscosity help's it stick to the things is should be lubing like the stanchions and the coil. Fork lubrication is a hydrodynamic system that results in complete separation of the fork stanchions from the internal bushings by a film of oil. The oil pools in the lowers and is pumped during compression up to the bushings. The upper seals act to block the ingress of dirt and outflow of the bath oil while the underlying foam rings stay saturated with oil from the bath to also provide that film of oil on the stanchions.
As you may infer, the physical characteristics like lubricity and viscosity of the oil are important considerations to the design and function of fork lubrication system. A 15W oil has a thinner viscosity than a 30W. The viscosity of the bath oil was an important consideration in the design and function of the fork's lubrication system. Inside the fork, the spring side and it's pumping system was designed around this weight of oil. Aspects such as how oil is pumped up to the bushings, the clinginess of the oil to the stanchions and bushings and the changes in viscosity related to heat buildup are all influenced by the viscosity. Using the called for weight of oil in the bath is important in the overall functioning and life of the fork.
Some may tell you that for the lower bath any oil will do. That's not the case and never has been. Oils other than spec can have additives that cause seal swell and increase stiction. They may not provide proper lubrication as they heat up. Other physical properties of a foreign oil can be detrimental to the function or life of the fork.
Some reasons for the 2 different bath oils between damper and spring side include a need to prevent mixing of the bath oil and damper fluid on the damper side. Since a damper's functional characteristics are highly dependent on the character of the damper oil, you wouldn't want to introduce a different oil with different properties into it. Using the same oil for the bath as what is used inside the damper, precludes problems should the damper ingest some bath oil.
Another reason would be the way the oil is pumped. There's a lot more stuff filling the damper side, so perhaps there is smaller orifices to handle the bath oil. That would perhaps call for a thinner oil to effectively pump up to the bushings and foam rings where it's to do the job of hydrodynamic lubrication of the stanchions.
While I cannot say for sure why the Charger damper side calls for a different bath oil (I'm most familiar with Fox), I can unequivocally state that there are myriad reasons to use the correct oil in the correct amounts in the correct places in today's suspension forks.