This study investigates how smart charging and vehicle-to-grid (V2G) technologies affect the European energy system in the 2050 under climate target constraints. Using an energy system model that explicitly represents EV batteries, charging infrastructure, and investment costs, we analyse passenger EVs within a broader context including power, heat, and industry sectors. The results show that coordinated charging is essential to limit infrastructure deployment, while V1G and V2G utilisation strongly depend on grid development. V1G provides the largest cost savings, with grid expansion and smart charging offering additive benefits. V2G adoption is highly context-specific: infrastructure costs influence both its utilisation and market value, and the additional charging required is limited to 14\%, supporting widespread adoption without overloading batteries. V2G contributes to winter peak supply in countries with seasonal gaps and stores excess PV generation during summer. Neglecting infrastructure costs can distort charging schedules and market signals. Overall, the study highlights the importance of coordinated charging and realistic infrastructure modelling to unlock EV flexibility and support system decarbonisation.