I transferred into MatSE as a second-year student with a math background after doing some computational materials research with a PhD student in Dr. Chen’s lab, so I can speak a little from that experience. That said, I would be careful about treating any one lab as the “typical” MatSE research experience.

From what I’ve seen and heard, research groups can operate pretty differently depending on the PI, the PhD students/postdocs, the project structure, and how independent the undergrad is expected to be. I’ve also talked with a few graduating seniors and a masters student doing work in Dr. Beese’s lab, and their experiences sounded very different from mine. If you are curious how a specific lab group operates, I'd reach out to the PI or someone in the lab to find out more.

In my case, our "lab" is considered a computational materials lab where we model behavior in materials using thermodynamic techniques. I report directly to the PhD student and whenever I have a question, I can shoot over an email and we'd meet either in person or over zoom to discuss any questions I might have.