Hi,
I think you are misunderstanding the use of that tool.
I don’t see any tags in most of your CPT, nor you have any listing for a lot of those CPT.
The sync tags tool, doesn’t copy tags from 1 CPT to another. It only corrects inconsistencies between wp terms table and the custom GD tables if any.
For the Search widget problem, it appears to be a server problem. The console is reporting a 500 internal server error when trying to save the search widget. Please contact your server support and report the problem to them. We would need at least to know what error is blocking the server to see if we can help.
In our demos this is not happening, so I don’t think it is a problem of our script.
Thanks