Standard errors you can report

The influence-function standard error can be too small or too large when a working model is wrong. See why, and compare it with the bootstrap and the full sandwich in four nuisance cases.

Further reading: Lunceford and Davidian (2004), Stratification and weighting via the propensity score in estimation of causal treatment effects, Statistics in Medicine 23:2937–2960; Hirano, Imbens and Ridder (2003), Efficient estimation of average treatment effects using the estimated propensity score, Econometrica 71:1161–1189; Funk et al. (2011), Doubly robust estimation of causal effects, American Journal of Epidemiology 173:761–767; Stefanski and Boos (2002), The calculus of M-estimation, The American Statistician 56:29–38; Efron and Tibshirani (1993), An Introduction to the Bootstrap, Chapman & Hall. Repeated-study numbers are precomputed by scripts/standard-errors-precompute.cjs (seeded); large-sample limits are exact calculations from the known law.