A workaround for the ArcMap equivalency issue is to customize the Quick Access Toolbar (top left of ArcGIS Pro) and add the Enable Enterprise Geodatabase GP tool to the toolbar. Like the right-click in ArcMap, a click starts the GP tool in AGP.
As I have already confirmed in other post, we don’t prefer to spend our life with workaround. We need to work with the same level you have been offering you guys in ArcMap.
Right-clicking does make sense much more Quick Access Toolbar in this case!
Understand where you're coming from. ArcMap has been in existence publicly for 20 years now with a year or two before public release for development. So 22 years if you think about it. It's a mature product that over time has had new functionality added to it. ArcGIS Pro is about 5 years into public release and does not have 100% functional equivalency but it's getting there with each release. As mentioned in a previous response, AGP developers/teams are genuinely reading and answering these GeoNet threads and value the information provided. I hope the next release of AGP addresses this idea!
If we compare the years of public availability between the two applications and understand that ArcMap is riding out its sunset years at this point, then ArcGIS Pro should be settling down and looking to become a stable, productive member of society pretty soon, no? We all take different paths, and I'd say it has come a long way - with some personal growth still ahead.
I came to the same conclusion that this was missing from ArcGIS Pro independently, and was referred to the Idea by Esri Technical Support, who I understand has been working to log an ENHancement request - apparently this was not added in version 2.5 of ArcGIS Pro. I'll provide more information as it's available, and maybe we'll see this at 2.6, or at least by the time Pro reaches those middle years...
Logged today by Esri Technical Support: #ENH-000129413 [Enhancement] Access the "Enable Geodatabase" option by right clicking on a database connection in ArcGIS Pro
