The advent of the web has led to a paradigm shift in the financial relations, with the real-time dissemination of news, social discourse, and financial filings contributing significantly to the reshaping of financial forecasting. The existing methods rely on establishing relations a priori, i.e. predefining graphs to capture inter-stock relationships. However, the stock-related web signals are characterised by high levels of noise, asynchrony, and challenging to obtain, resulting in poor generalisability and non-alignment between the predefined graphs and the downstream tasks. To address this, we propose GAPNet, a Graph Adaptation Plug-in Network that jointly learns task-specific topology and representations in an end-to-end manner. GAPNet attaches to existing pairwise graph or hypergraph backbone models, enabling the dynamic adaptation and rewiring of edge topologies via two complementary components: a Spatial Perception Layer that captures short-term co-movements across assets, and a Temporal Perception Layer that maintains long-term dependency under distribution shift. Across two real-world stock datasets, GAPNet has been shown to consistently enhance the profitability and stability in comparision to the state-of-the-art models, yielding annualised cumulative returns of up to 0.47 for RT-GCN and 0.63 for CI-STHPAN, with peak Sharpe Ratio of 2.20 and 2.12 respectively. The plug-and-play design of GAPNet ensures its broad applicability to diverse GNN-based architectures. Our results underscore that jointly learning graph structures and representations is essential for task-specific relational modeling.