As someone who cut their teeth in embedded before going into web development, I've seen a significant amount of similarities between the two. The most obvious to me is that now we spend a lot of time connecting prebuilt libraries together - back in the day we wrote everything from scratch. The skills required to interface to a bluetooth library are not any different to say connecting to a map API on a web page... if it all works and does what it says in the docs. At some point your core skills and experience are required in the specific domains to identify and fix bad behaviour (i.e. your bluetooth library isn't working because you have physical antenna issues etc).

There is also a large amount of crossover as embedded gains more resources. Often you're working with javascript because your device needs to have an embedded web server with custom functionality. Sometimes you see SQlite on embedded flash, although debatable if they really needed it. Running Linux is far more common and it works pretty much the same regardless if it's on an MCU or a VM in the cloud.

The main difference I see is to do with the ease of fixing mistakes in the field. With web development I can usually git push and the issue is fixed for all users. With embedded, I almost never have an internet connection so it's a case of physically sending people to site or product recall to fix the issue if it's serious. Internet connections are becoming more common in embedded so we can remote update, but still the minority in general.

Lots of common ground, but just like any discipline it's that last 20% that makes the difference.