For BSEM, software wise I recommend to use blavaan in R, it uses the same syntax of lavaan, and runs the model in either Stan or JAGS. I teach a summer week course on the topic BSEM summer course, which will be a webinar format this summer due to COVID-19

blavaan has the advantage of being pretty flexible for a wide variety of models, while still makes it easier to work on

For IRT, I have built my model syntax, for easiness you can look at the edstan package edstan which can run several IRT models in Stan. Might be limited if you want to run a model that is not available there

Even with shrinkage you will be looking at item effects, instead of a major factor. And each item has multiple sources of variance that can affect the relation (X = C + M + O + S + e). I dont think shrinkage would correct for measurement error either

These are some references

Garnier-Villarreal, M., & Jorgensen, T. D. (2019). Adapting Fit Indices for Bayesian Structural Equation Modeling: Comparison to Maximum Likelihood. *Psychological Methods* . https://doi.org/dx.doi.org/10.1037/met0000224

Luo, Y., & Jiao, H. (2018). Using the Stan Program for Bayesian Item Response Theory. *Educational and Psychological Measurement* , *78* (3), 384â€“408. https://doi.org/10.1177/0013164417693666

Merkle, E. C., & Rosseel, Y. (2018). \textttblavaan: Bayesian structural equation models via parameter expansion. *Journal of Statistical Software* , *85* (4). https://doi.org/10.18637/jss.v085.i04

Merkle, E. C., & Wang, T. (2018). Bayesian latent variable models for the analysis of experimental psychology data. *Psychonomic Bulletin & Review* , *25* (1), 256â€“270. https://doi.org/10.3758/s13423-016-1016-7

MuthĂ©n, B., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. *Psychological Methods* , *17* (3), 313â€“335. https://doi.org/10.1037/a0026802

van de Schoot, R., Kluytmans, A., Tummers, L., Lugtig, P., Hox, J., & MuthĂ©n, B. (2013). Facing off with Scylla and Charybdis: A comparison of scalar, partial, and the novel possibility of approximate measurement invariance. *Frontiers in Psychology* , *4* . https://doi.org/10.3389/fpsyg.2013.00770

Kaplan, D. (2014). *Bayesian Statistics for the Social Sciences* . New York:\ The Guilford Press.

Lee, S. Y. (2007). *Structural Equation Modeling: A Bayesian Approach* . Wiley. https://books.google.com/books?id=f6kquAAACAAJ

Reckase, M. D. (2009). *Multidimensional Item Response Theory* (1st ed.). Springer Publishing Company, Incorporated.