I can't speak for assembly. I did learn some WebAssembly, and I found it quite interesting to think in a very low-level way and in a quite different style of programming.
I haven't really used the knowledge directly in my working life, just for my toy programming language. But I work in Java - maybe if you do low-level performance stuff it'll be more directly applicable. (Your profile says front-end, but you also asked about C, so maybe?).
However, new ways of thinking can be at least as useful as lines of code you can use directly. If you have the time and interest, I'd say doing something totally new like assembly would be great.
It is my understanding that 'normal' assemblies are fairly different from webassembly (correct me if I'm wrong), but I would expect it'll teach similar lessons. Or since you're a front-end dev, maybe WebAssembly is even more interesting?