In the ArcGIS Online Map Viewer, when you add content, you can search in My Content, My Organization, Living Atlas, or ArcGIS Online. From ArcGIS Pro, you search My Content, All Portal (My Org), and Living Atlas.
Is there a way to search for ArcGIS Online content that is not in your organization and is not included in the Living Atlas? The only workaround I have is to search for it in ArcGIS Online, find the item page, copy the URL, and then Add Data from Path in Pro.
In ArcGIS Pro, if you're signed in to an ArcGIS Enterprise org, you can't search ArcGIS Online content. But if you're signed in to an ArcGIS Online org, you can. On the Catalog pane, click the Menu button and uncheck Search My Organization.
This experience will be better when ArcGIS Pro 2.6 is released... tomorrow. In the 2.6 user interface, all the search locations (My Content, My Org, ArcGIS Online, etc.) will be visible from the Catalog pane.
The 2.6 web help is online now. If you want to see what the new UI looks like, have a look at the Search portal items topic.