It’s the distribution pymc_experimental.distributions.timeseries.DiscreteMarkovChain. Again, you can basically just copy-paste the first example in the notebook I linked (cell 8). Replace pm.sample with pm.sample_prior_predictive, and replace P with your transition_matrix. I’m happy to look at your code if you run into issues.
I’m not sure I understand this. MCMC is an algorithm for evaluating integrals, not for simulating systems with discrete Markov dynamics (also called “Markov Chains”). You will not be using MCMC at all for the problem as stated, because you aren’t doing any inference.