Modern financial systems depend on complex digital data pipelines that support regulatory reporting, enterprise analytics, and AI-driven decision-making. However, trust in these systems cannot be achieved through policy and audit alone, particularly in environments characterised by automated transformations, distributed ownership, and high-velocity data movement. This paper introduces a governance-embedded finance digital data foundation that unifies stewardship, privacy-by-design, lineage, and data observability as core architectural capabilities. The proposed framework shifts governance from static oversight to continuous verification by making control effectiveness observable at runtime. Using enterprise-scale case evidence from real-world financial data ecosystems, the paper demonstrates how observable governance improves audit readiness, strengthens provenance for explainable analytics, reduces time-to-detect and time-to-remediate data issues, and increases stakeholder confidence in AI-driven insights. The paper concludes by outlining research directions for real-time governance observability, AI-assisted stewardship, cross-domain validation, and standardised governance maturity models.