Where the feature store fits into the overall ML lifecycle depends on the functionality of the feature store. Some feature stores are purely for storing and retrieving batch datasets. With these kinds of feature stores, they would likely be used after an ETL job from a data engineer to store the newly transformed data or after a feature engineering job from a data scientist to store the newly created features. From there, the end user can browse the feature store and see what is available to retrieve. Because this feature store is purely for storing and retrieving features, it has more limited uses within the overall ML lifecycle.
Some more advanced feature stores support batch and real-time transformation engines, real-time feature serving, and model monitoring integration. This allows the feature store to be used throughout the entire ML lifecycle from data ingestion/transformation, mode training, model deployment, and model monitoring. Keeping all of these processes centralized in a single place allows for standardization across an organization as well as glue-less integration between different aspects of your ML lifecycle.