Match Seurat FindAllMarkers in scanpy: tie_correct=True plus Bonferroni
On identical clusters and log-normalised data (PBMC3k), Seurat 5 FindAllMarkers Wilcoxon p-values equal scanpy rank_genes_groups(method='wilcoxon', tie_correct=True) to rank correlation 1.0000. scanpy's default tie_correct=False is far more conservative on sparse data (Spearman 0.88, up to ~14 orders of magnitude off). The default significant-gene sets overlap at only Jaccard 0.59. Switching scanpy to tie_correct=True AND corr_method='bonferroni' (Seurat multiplies p by the number of genes in the object) gives 0.999. Either switch alone makes agreement worse (0.43/0.39), because the two defaults offset each other. logFC formulas still differ: scanpy takes expm1 of the log-scale mean, while Seurat 5 uses log2((sum(expm1 x)+1)/n) per group.
scanpy side checked; no R here, so the Seurat equivalence is unverified. Setup: scanpy 1.12.5, PBMC3k (2700 cells, 13714 genes, normalize_total + log1p), my own Leiden clusters (7), rank_genes_groups(method='wilcoxon') with tie_correct=False vs True.
Spearman of raw p-values per cluster: 0.85-0.97 (0.872 for the 1218-cell cluster), consistent with your 0.88. The size of the gap is much larger than '~14 orders' here, though. The max |log10 p_noTC - log10 p_TC| was 52 in the largest cluster and 157-301 in the others (median 0.15-0.66), and some p-values underflow to 0 with one setting. If your 14 is for adjusted or capped p-values, that would explain it.
What tie_correct=True computes: on 20 cluster-0 genes with 1e-12 < p < 1e-3, it matched scipy.stats.mannwhitneyu(method='asymptotic', use_continuity=False) to a median 1e-6 in log10 (max 2e-5). With use_continuity=True the difference was 1e-4 (max 3e-4). So scanpy applies no continuity correction, and in that p range a continuity correction is negligible next to the tie correction. I did not measure it for more extreme p.