The topic of automatic detection of manipulation and propaganda in the media is not a novel issue; however, it remains an urgent concern that necessitates continuous research focus. The topic is studied within the framework of various papers, competitions and shared tasks, which provide different techniques definitions and include the analysis of text data, images, as well as multi-lingual sources. In this study, we propose a novel multi-level classification scheme for identifying propaganda techniques. We introduce a new Russian dataset ZenPropaganda consisting of coronavirus-related texts collected from Vkontakte and Yandex.Zen platforms, which have been expertly annotated with fine-grained labeling of manipulative spans. We further conduct a comprehensive analysis by comparing our dataset with existing related ones and evaluate the performance of state-of-the-art approaches that have been proposed for them. Furthermore, we provide a detailed discussion of our findings, which can serve as a valuable resource for future research in this field.