I have a Page Library in my Authoring Site. The Pages are from the Content-Type myArticlePage. (I have filled all Custom SiteColumns of this ContentType in a view Pages with valid values, made a Index-Reset and a Full-Crawl [several times]). Also published this Page Library as Catalog. Next thing i tried to do is to make a publishing site. At this site i did insert a content by search webpart which i configured to populate all pages. I wanted to limit this by content type MyArticlePage but it does not show up in the list. How do I get this Content Type form my Authoring Site into my Publishing Site?
You should use a Result Source based on your Catalog to limit the scope of items returned by the Content Search Web Part. The result source is created automatically when you enable a list or library as a Catalog. For more information, see this page: https://docs.microsoft.com/en-us/sharepoint/administration/stage-9-configure-the-query-in-a-content-search-web-part-on-a-category-page#BKMK_AboutTheQueryConfiguration
If you want to make a Content Type available to multiple sites in a single site collection, define the Content Type at the Root Site Collection using Site Columns. Content Types created this way are available to all child sites in the same collection.
If you want to publish a Content Type from one Site Collection to another, you should enable Content Type Syndication on the source Site Collection. Here is an article about how to do that: https://support.office.com/en-us/article/publish-a-content-type-from-a-content-publishing-hub-58081155-118d-4e7a-9cc5-d43b5dbb7d02