R has a package called sure, which uses SUrrogate REsiduals for diagnostics associated with cumulative link ordinal regression models. The package can be used to detect model misspecification with respect to mean structures, link functions, heteroscedasticity, proportionality, and interaction effects. It doesn't look like Stata has anything similar implemented.
To learn more about the package functionality, you can refer to the research article Residuals and Diagnostics for Binary and Ordinal Regression Models: An Introduction to the sure Package by Greenwell et al. (The R Journal Vol. 10/1, July 2018), which you can find here: https://journal.r-project.org/archive/2018/RJ-2018-004/RJ-2018-004.pdf.
The surrogate approach to defining residuals for an ordinal outcome Y was introduced in the paper Residuals and Diagnostics for Ordinal Regression Models: A Surrogate Approach by Dungang Liu and Heping Zhang (Journal of the American Statistical Association vol. 113,522 (2018): 845-854). The idea underlying this approach is to define a continuous variable S as a “surrogate” of Y and then obtain residuals based on S. The paper is available here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133273/.