Accurate flood extent and depth information are essential to emergency response, yet most existing studies treat these tasks separately. This work introduces an integrated SAR-to-depth framework that combines water body semantic segmentation with DEM-based geometric depth estimation to generate both flood-extent maps and pixel-wise depth products from Sentinel-1 imagery. For flood extent mapping, we propose a cross-scale Mamba with selective state-space blocks, which achieves a mean IoU of 79.8% across ten European flood events from the KuroSiwo benchmark, outperforming RSMamba by 7.4% and surpassing common CNN baselines. The experimental results demonstrate that the proposed model also generalizes well to unseen events, with test performance exceeding validation scores. When both CS-Mamba predictions and KuroSiwo reference masks are input to FLEXTH, the resulting depth estimates agree within ±2% across four global DEMs. Initial validation against ICESat-2 altimetry using MERIT DEM (19 matched points) shows RMSE of 4.60 m and Bias of -1.88 m, providing preliminary validation evidence with systematic underestimation. Systematic DEM comparison shows FLEXTH is robust across all four DEMs, with Copernicus and MERIT showing closest agreement with reference mask estimates. The framework produces three-class flood masks and pixel-wise depth maps, combining extent mapping with quantitative depth information for operational flood monitoring.