I've looked at it today as well, for most of the day. Embedded tomcat doesn't have a webapps directory, whereas the full version of tomcat does, so the PoC writes the webshell to webapps/<APP>/tomcatwar.jsp and that is served up then.
I'm on OSX and I found the temp directory that is created for the embedded tomcat at runtime but there's nothing deployed there, so I can't figure out where to write the webshell to or if it is even possible. I looked at the process with lsof and just followed the trail to find the directory but it's not working.
Anyway, embedded tomcat IS vulnerable, just not sure if it is exploitable.
To check if it is vulnerable you can do run the following curl command: curl "http://localhost:8080/?class.module.classLoader.URLs%5B0%5D=..."
If this returns status:400 then it is vulnerable, if not then it is not. If you have an app deployed to a different context path (so /my-webapp) then you'd need to run: curl "http://localhost:8080/my-webapp?class.module.classLoader.URL..."
I don't think it is common to use @RequestMapping in java and take in a POJO as a parameter to the request, but that is needed in order to be vulnerable to this.
I'm sure there's other gadgets that can be used to exploit this, the example we saw was using tomcat to write a webshell.