This is an excellent test. Could you share it on Stackblitz so I can play with it a bit?
One clarification I got from the Angular team is that providedIn: "platform" was designed mostly for internal Angular services such as Router.
It seems that the documentation on that option is misleading in the sense that Angular Elements or multiple apps were not the intended target for this option. I'm going to investigate this a bit further and let me know my findings.
Could you try your example using "providedIn: root" instead of platform and see how it goes?