I noticed there were quite a few threads regarding this subject. But none of them contained any information that solved my issue tonight. All of a sudden, the Add to Any window would not display upon mouseover hovering, but the ATA share and save options would appear in a new web browser window (in large Mama style). It didn't make sense to me that one had to insert code snippets here and there in .php files or test the issue in another theme, etc... I think many Forum users failed to recognize that maybe your anti-tracking module is/was the culprit by blocking Add to Any from displaying the share/save window. That's what I discovered. One has to troubleshoot issues going through a list of very basic culprits first, then move on to the more exotic experiments and solutions. I'm fortunate enough to have delved for 10 years as a support engineer for a popular 3D SW product developer. But that was in another life ;).
Please pass this info along to whomever can benefit from it.