The Covid-19 pandemic has sparked renewed attention on the prevalence of misinformation online, whether intentional or not, underscoring the potential risks posed to individuals' quality of life associated with the dissemination of misconceptions and enduring myths on health-related subjects. In this study, we analyze 6 years (2016-2021) of Italian vaccine debate across diverse social media platforms (Facebook, Instagram, Twitter, YouTube), encompassing all major news sources - both questionable and reliable. We first use the symbolic transfer entropy analysis of news production time-series to dynamically determine which category of sources, questionable or reliable, causally drives the agenda on vaccines. Then, leveraging deep learning models capable to accurately classify vaccine-related content based on the conveyed stance and discussed topic, respectively, we evaluate the focus on various topics by news sources promoting opposing views and compare the resulting user engagement. Aside from providing valuable resources for further investigation of vaccine-related misinformation, particularly in a language (Italian) that receives less attention in scientific research compared to languages like English, our study uncovers misinformation not as a parasite of the news ecosystem that merely opposes the perspectives offered by mainstream media, but as an autonomous force capable of even overwhelming the production of vaccine-related content from the latter. While the pervasiveness of misinformation is evident in the significantly higher engagement of questionable sources compared to reliable ones, our findings underscore the importance of consistent and thorough pro-vax coverage. This is especially crucial in addressing the most sensitive topics where the risk of misinformation spreading and potentially exacerbating negative attitudes toward vaccines among the users involved is higher.