Do you have raw individual data with 0/1 responses in each study? If so, you can use each study as a group indicator in random intercepts and slopes in binary regression with mixed effects. If the studies have multiple measurements on each patient, you can also have two layers of nested random effects lme4::glmer(y ~ treatment * time + (1 | study/patient), family = binomial) or use conditional fixed-effect estimator such as survival::clogit in R. Baseline characteristics should be added as predictors even if treatment assignment was random because it will reduce the standard error of treatment effect.
If individual data are not available, it will be difficult to compare treatment efficacy. Binary regression coefficients from summary tables are not usable across different studies because they are standardized by an unknown factor that varies among different models. See Williams, R., & Jorgensen, A. (2023). Comparing logit & probit coefficients between nested models. Social Science Research, 109, 102802. https://doi.org/10.1016/j.ssresearch.2022.102802. We will need to translate model coefficients into average marginal effects on probability. This requires at least the variance-covariance matrix of model coefficients. Because logit and probit are nonlinear transformation, the effect of treatment on the event probability is also nonlinear in dosage and dependent on the value of other predictors. Thus, for binary regression models among different studies to be comparable, we need to state the effect in terms of the changes in event probability between treatment groups at specific values of other predictors (e.g., age, sex).