Hi,
Elementor doesn’t recognize WP Customer Area: What does that mean? What would you expect exactly? I’ve never tried Elementor + WP Customer Area, I wouldn’t see any need for that.
For me, Elementor should be used for rendering page layouts, not post contents, but I might be wrong in some cases.
However, if you try to add Elementor’s widgets or third-party plugins’ elements into the area, you’ll need to check that code snippet: Disable CSS resets and allow integration of third party plugins
This would allow an external CSS component to be correctly integrated into your private area.
Regards.