In recent years, the global energy sector has seen significant transformation, particularly in Europe, with a notable increase in intermittent renewable energy integration. Italy and the European Union (EU) have been among the leaders in this transition, with renewables playing a substantial role in electricity generation as of mid-2020s. The adoption of Battery Energy Storage Systems (BESS) has become crucial for enhancing grid efficiency, sustainability, and reliability by addressing the intermittent renewable sources. This paper investigates the feasibility and economic viability of batteries into wholesale electricity markets as per EU regulation, focusing on the dynamics of very different markets, namely the Day-Ahead Market (DAM) based on system marginal price and the Cross-Border Intra-day Market (XBID) based on continuous trading. A novel model is proposed to enhance BESS operations, leveraging price arbitrage strategies based on zonal price predictions, levelized cost of storage (LCOS), and uncertain bid acceptance in continuous trading. Machine learning and deep learning techniques are applied for price forecasting and bid acceptance prediction, respectively. The study finds that data-driven techniques outperform reference models in price forecasting and bid acceptance prediction (+7-14% accuracy). Regarding market dynamics, the study reveals a higher competitiveness of the continuous market compared to the DAM, particularly with increased risk factor in bids leading to higher profits. This research provides insights into compatibility between continuous markets and BESS, showing substantial improvements in economic profitability and the correlation between risk and profits in the bidding strategy (+9 M€ yearly revenues are obtained with a strategic behavior that reduces by 60% awarded energy).