In the interest of providing a semi-general solution, you might check out the development version of the equatiomatic package, which recently added support for glmer models: GitHub - datalorax/equatiomatic: Convert models to LaTeX equations
If you can specify your model in lme4 with the glmer function, the output that equatiomatic provides may give you a good starting point. You’ll still need to specify priors in math notation for the top-level hyperparameters.