Knowledge graph generation typically relies either on predefined ontologies or on schema-free extraction. Ontology-driven pipelines enforce consistent typing but require costly schema design and maintenance, whereas schema-free methods often produce fragmented graphs with weak global organization, especially in long technical documents with dense, context-dependent information. We propose \textbf{TRACE-KG} (\textbf{T}ext-d\textbf{R}iven schem\textbf{A} for \textbf{C}ontext-\textbf{E}nriched \textbf{K}nowledge \textbf{G}raphs), a framework that jointly constructs a context-enriched knowledge graph and an induced schema without assuming a predefined ontology. TRACE-KG captures conditional relations through structured qualifiers and organizes entities and relations using a data-driven schema that serves as a reusable semantic scaffold while preserving full traceability to the source evidence. Experiments show that TRACE-KG produces structurally coherent, traceable knowledge graphs and offers a practical alternative to both ontology-driven and schema-free construction pipelines.