1. Cosma Shalizi has documented their own <A HREF="http://bactra.org/notebooks/ergodic-theory.html">pathway into ergodic theory</A>, with an eye towards applications in <A HREF="http://bactra.org/notebooks/dependent-learning.html">statistical learning theory</A> (but with many side branches). You might find the annotated bibliography helpful.

2. More specifically, I understand the question as being motivated by a plan to embark on original research at the interface of ergodic theory and stochastic analysis. For such a purpose it seems helpful if the topic is less mature, less well established, and perhaps less well covered by "landmark papers".    
One example: <A HREF="https://en.wikipedia.org/wiki/Ergodicity_economics">Ergodicity economics</A> is a branch of mathematical finance at this interface. A foundational paper is by <A HREF="https://www.nature.com/articles/s41567-019-0732-0">Ole Peters</A> (2019). There are intriguing connections with <A HREF="https://ergodicityeconomics.com/2023/10/20/an-ergodicity-perspective-on-reinforcement-learning/">machine learning.</A>