Bad r-hat on intercept only

That may or may not be affecting convergence. But the main issue that would concern me is not so much the large number of parameters, but the large number of variables in the expectation. Their dependencies may be creating spurious associations which may distort the estimate or over/under-estimate uncertainty. I don’t know how your variables relate to each other, but it’s usually a good idea to have a very good theoretical and practical notion of how variables may associate to each other (i.e. do variable x has an effect on variable z and variable y (or vice-versa) and what type of effect? Is it a chain, a fork, a collider? If so, is it a good idea or a bad idea to condition on z if I want to know the effect of x on y?, etc.). You’ll find more info on these topics in the links I shared on my firs reply.