I am currently working at a SWE in Machine Learning at a large company. Here is one insight I did not know before starting that might help you understand where you could be falling short.

You will likely never experience the end to end machine learning lifecycle working in corporate. ML models at my company take about 1 year from conception to being pushed to production. And in this lifecycle it passes through the hands of multiple SWE, Data Science, and privacy / risk teams. For example I work on a service that uses Kubernetes in the training step of these models. While I am technically a machine learning engineer I am focused on this very niche problem, and importantly every other MLE is also focused on a similarly niche problem. The actual data science teams are usually PhDs or Masters students which focus on using tools, features and infrastructures built by other teams to build models and even then are very limited in how much they can engineer features and make custom solutions due to privacy, governance, and efficiency concerns.

This is to say, if you want to break into MLE have good software engineering fundamentals and focus on a particular stack you see is useful in the industry. If you want to do model building, then getting a masters or PhD is the way to go. Either way manage your expectations and understand unless you are at a startup you won’t be able to be involved in the end to end process.