Thanks for checking that, i suspect there is something to do with the GLM like DGP you have there… not entirely sure. It’s perhaps worth noting that packages in R like ivtools have a distinct class for estimating IVs with GLMS: https://cran.r-project.org/web/packages/ivtools/ivtools.pdf
You could try stripping back your DGP to just the linear statements or use a dataset that works with the linear framing and then overlay Logit transforms and try and see when it breaks…
I think some simulation will help an maybe worth trying other estimation strategies that don’t rely on the linear phrasing e.g. maybe try the GMM method. Or try g-computation approaches… so ignore the parameter estimates (as they mislead) but instead try imputing the outcome under counterfactual settings for the treatment variable an take the difference of the imputed values. Ivtools above uses g-est strategies which i think must be a g-computation non-parametric estimation routine… but i haven’t dug into the R code…