What can pay-off is learning to read C. Node.js, Firefox, Postgres, Linux are all written in C/C++ so if you ever want to really understand what's going on or have to debug a nasty bug, then you will need to be able to find your way around these code-bases.
E.g. I think the size of my WASM demos is quite reasonable for what they do:
https://floooh.github.io/tiny8bit/
https://floooh.github.io/sokol-html5/
However, AssemblyScript is also a pretty good choice for this type of stuff from what I'm hearing (while for instance languages with a complex runtime like C# are not).
These are things that are not directly useful, but help you have a better mental model of how your language of choice actually works.
I think it’s good to at least play with C and understand how memory management and pointers in C work, but I don’t think I would recommend you go out of your way to learn C or spend any significant amount of time writing it. At the end of the day it’s just another tool in the toolbox. I would recommend the book Code, by Petzold, if you want to really want to explore computers at a low level in a friendly format.
Directly to machine code, not assembly.
-Embedded/cyber-physical systems software (firmware dev)
-Driver development (applies to Win/macOS/UNIX/iOS/Android)
-Contributing to the Linux kernel/OS dev in general
-Contributing to many large OSS projects (Apache, ffmpeg)
-Exploit/malware dev/reverse engineering
-Emulator development
you'd need to learn C.
Is it useful as a web developer? Only if you want to write extensions to Python in C or step away from the web developer label and learn systems programming.