I kind of moved the other direction and worked with people like you moving from "high level" development to embedded.
The first thing to note is that "Embedded" is a very wide area, a lot of it is not too special and you might continue doing web development as you are used to, maybe with small adjustment of how you load, debug and communicate with your device.
It's the lower layers, mainly device drivers and BSP (Board Support Package) but even some algorithms close to the hardware or special optimizations, where things becomes interesting and requires specialization.
I worked on those lower layers and have found myself more than once debugging "real software" using a logic analyzer or other Electrical Engineering tools to catch a software problem.
How did it go for those transitioning "down" into embedded? usually quite well, you will need to catch up with the technology, learn some new concepts and make a change in the way you think of things, for example memory or multi processing, but it is definitely doable and enjoyable.