Existing Vision Foundation Model (VFM)-based iterative stereo pipelines under-exploit three information pathways: multi-scale backbone features are collapsed into single-level correlations, geometric priors remain untapped at initialization, and context propagates only locally. These gaps widen under degraded photometric cues, making underwater scenes a stringent generalization test. To address this, we propose LinStereo, built upon Depth Anything V3, whose core is a Position-Aware Linear Attention (PALA) module that replaces local recurrence with global aggregation at linear cost, propagating reliable estimates from well-matched regions into degraded areas while preserving disparity structure. PALA is made effective by two enabling components: Hierarchical Semantic Cost Volumes (HSCV), which supply scale-aligned correlations from the VFM feature hierarchy, and a Depth Prior Initialization (DPI) that converts monocular depth into a metrically calibrated warm start. LinStereo achieves state-of-the-art-level accuracy on standard benchmarks and strong cross-domain generalization, particularly on underwater scene where severe photometric degradation makes stereo matching particularly challenging, attaining the best overall accuracy with consistent gains 28% lower AbsRel on TartanAir-UW, 26% on SQUID, a real-world underwater dataset).

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