What does it usually mean when a late stage startup offers a way average base salary that's much higher than public companies?

This is pretty standard. When a startup matures and becomes profitable, founders no longer need to offer precious equity to attract great talent. It's cheaper to simply pay better wages.

So yes, your equity will likely be very minimal because you aren't taking on the risk of earlier employees who sacrificed job security (and wages / benefits) for delayed gratification.