Just out in Statistics in Medicine, this is a helpful review of approaches to adjusting for observed confounding in non-randomised evaluations (and other studies). Includes a concise summary of assumptions, using the Neyman–Rubin potential outcomes framework.
Keele, L., & Grieve, R. (2025). So Many Choices: A Guide to Selecting Among Methods to Adjust for Observed Confounders. Statistics in Medicine, 44(5), e10336.