Wine alcoholic fermentation occurs in a dynamic biochemical environment where interactions between the vessel and the product can cause inorganic and organic species to migrate into the fermenting must or wine. At low pH and with rising ethanol levels, fermentation tanks made of stainless steel, concrete or cementitious materials, ceramics, or polymers exhibit material-specific behaviors that may promote the release of toxic trace elements or alter technologically important ions. These changes can affect yeast physiology, fermentation kinetics, and matrix stability, directly impacting wine safety and quality. They may also influence the evolution of key fermentation metabolites and phenolic constituents, thereby affecting process performance, color development, oxidative stability, and other quality-related attributes. This review synthesizes current evidence on migration mechanisms and examines how vessel composition shapes the chemical and microbiological profile of fermentation. It also critically evaluates biosensor technologies—covering both biorecognition elements and signal-transduction strategies—and assesses the transition from laboratory prototypes to in situ or at-line implementations capable of detecting both migration-related events and process-relevant compositional changes with operational value for HACCP-based control. Electrochemical, optical, bienzymatic, and nanozyme-enabled platforms are discussed in terms of selectivity, matrix compatibility, and long-term functional stability under polyphenol and protein interference, CO₂ variability, fouling and biofouling, and calibration drift. Particular attention is given to analytes associated with vessel-derived migrants and to biosensor targets related to fermentation metabolites and phenolic indicators, which support dynamic process monitoring and quality-focused decision making. Considering regulatory compliance requirements across the EU, US, and Asia, we propose a practical pathway for integrating biosensors into HACCP monitoring by treating vessel–product interactions as critical control points, while laboratory reference methods remain essential for verification and compliance documentation.