Interesting, thanks for the reply.
I might be misunderstanding you, but this is not my experience (at least in VS Code). Using VS Code, I have never imported arcpy.management, arcpy.analysis, arcpy.cartography, etc. in my tools.
I have also never seen reference to this import syntax in Esri documentation. This and the anecdotal evidence below make me skeptical that I need to "import arcpy.management".
In VS Code, intellisense from base arcpy import:
also getting intellisense for management functions with this import style:
This is also not how other modules work, at least for me in VS Code. I don't import numpy.random for intellisense regarding "randint".
or in PyCharm.
Would love to hear other ideas, if you have them. This feels like a PyCharm problem/setting, or something to do with the way ArcPy is written and interpreted by PyCharm, not an import style problem.