The documentation of MCMCChains.rhat references the paper https://arxiv.org/pdf/1903.08008.pdf
from which it apparently takes the calculation of rhat (and ess?).
I have only skimmed over the first two pages just now, and hope I do understand correctly. The authors make the point that in general the convergence of MCMC cannot be reliably assessed from a single chain.
Thus, those observables are not calculated for every chain separately, which explains the identical values you observe. You may force a split by calling ess_rhat(chains[:,:,1]) etc., but again, those might not reliably report failed convergence and overestimate the ESS.
(P.S.: Please do not double post 'ESS' in Turing.jl if a question doesn’t receive any attention for a couple of days. That happens. Instead, you can bump it with a comment after a while.)