Hi Nate! Chao1 is a valid estimate of total species richness only when all species are equally abundant -- unlikely to be the case! breakaway is a good tool.
@Pauline_Trinh wrote an awesome tutorial so do reach out if you have questions or feedback. breakaway's models are pretty flexible and statistically rigorous so gives error bars, too, of course! In the R version of breakaway, we also have a method for hypothesis testing that uses those standard errors -- I encourage you to check it out.