The rapid growth of Electric Vehicle (EV) adoption has intensified the need for investments in public Charging Stations (CS). With growing needs of CSs sizes, distribution system operators and national regulatory authorities are increasing the Grid Connection Power (GCP) costs. This is to steer investments on local Renewable Energy Sources - as Photovoltaic (PV) - and stationary Battery Energy Storage System (BESS) rather than on GCP. This trend, combined with the decreasing costs of BESS, introduces a complex challenge for investors when determining the optimal sizes for CSs. Since existing studies often overlook GCP costs, our study introduces a methodological framework for determining the optimal sizing of BESS and GCP for CSs, with a focus on the Italian context. In doing so, this work addresses two main concerns: the impact of costs and forecast (for EV demand and PV production) and the GCP-BESS cost relationship in the optimal asset cost breakdown. The proposed approach is framed as a security-constrained sizing model, coupled with sensitivity analysis and a level set evaluation. The findings of this research not only highlight the need for considering the GCP costs in similar sizing problems, but also the investment cost allocation in current and future scenarios.