Here is a patch with a fix.
As @erwinvb mentioned, the problem is that nested dialogs have the same data-drupal-selector attribute. Current patch adds also paragraph bundle to the attribute, to make it more unique. It will probably work for most cases, except when for some reason we have the same paragraph form opened in nested dialogs. This case will require each dialog to know how deep in the nesting level it is.
Current patch is a quick fix for the most people :)
I have the same need on a project, so here is the patch :)
Regarding #13 ✨ Add Preprocessor Loading for Suggestions Fixed , here is a patch that allows deeper pre-processing: https://www.drupal.org/project/preprocess/issues/3112575#comment-14882622 ✨ Deeper Preprocess Suggestions don't load without a Template or actual hook_preprocess RTBC
I came across the same need, and the solution seems pretty simple, just remove the check if such a template exists before pre-processing it. Maybe I didn't take into consideration some edge cases, will see later :)
Attaching a patch.