Not sure how much you've gotten into CL but online learning while similar is not the same.

Online learning is more akin to RL in that it's a structured and boxed enviroment. Step outside of that box or the box changes too much and you collapse.

CL is much more similar to meta learning. The concepts are more about learning NEW content while keeping previous the same.

CL is a completely open problem with all model types. EWC is amoung the better attempts (and a favorite of mine) at solving it with big limitations.