Emerging spatial omics technologies empower comprehensive exploration of biological systems from multi-omics perspectives in their native tissue location in two and three- dimensional space. However, sparse sequencing capacity and growing spatial resolution in spatial omics present significant computational challenges in identifying biologically meaningful molecules that exhibit variable spatial distributions across different omics. We introduce scBSP, an open-source, versatile, and user-friendly package for identifying spatially variable features in high-resolution spatial omics data. scBSP leverages sparse matrix operation to significantly increase computational efficiency in both computational time and memory usage. In diverse spatial sequencing data and simulations, scBSP consistently and rapidly identifies spatially variable genes and spatially variable peaks across various sequencing techniques and spatial resolutions, handling two- and three-dimensional data with up to millions of cells. It can process high-definition spatial transcriptomics data for 19,950 genes across 181,367 spots within 10 seconds on a typical desktop computer, making it the fastest tool available for handling such high-resolution, sparse spatial omics data while maintaining high accuracy. In a case study of kidney disease using 10x Xenium data, scBSP identified spatially variable genes representative of critical pathological mechanisms associated with histology.