I think you are on the right track. It may be that it doesn’t work with any custom post type, whatever the plugin or custom code that created it.
In one of my tests, I added the default WordPress Search widget to a sidebar and it added the social media icons to that widget as well. So, I’m wondering whether it’s messing with the other database records, as well. Unfortunately, I did not take a screenshot of that test.
The fix we came up with before your last posts was
Site 1: Go to Appearance -> Customize -> Post -> Social and chose Hide in the dropdown and check the Hide share buttons on static pages.
Site 2: The action in Site 1 stopped the social media buttons from appearing, but the Content Blocks were broken. I hardcoded the content into the template files. In a few minutes, I have a meeting with my client to show her how to go into the template files if she needs to make changes. This is not a possibility with many clients, but she is fearless.