There is no such consensus. Transformers navigate problem spaces with various mechanisms that include recursion, and multi-pass inference means the depth can be arbitrary. This means that models pick up on the functions that generate answers, not simple statistical relationships you see in Markov chains.

"Stochastic parrot" is a derogatory term and I've never seen anyone who actually understands the technology use that phrase unironically. If anything, it's a shibboleth for bias or ignorance.