Giant, obnoxious, and annoying indicator of what Portal you're logged into. Like Trunk Monkey.

[ThomasColson]

I just spent many minutes looking for something in my on-prem Portal while in Catalog Pane, only to discover I was logged into AGOL. I use enterprise login for both, so there is no "obvious" indication of what Portal I'm logged into unless I move my mouse over the name in the upper-right of the Pro UI and click on it. 

I think it should look like this when you're logged into Portal:

And when you're logged into AGOL

[KoryKramer]

I don't think this meets the requirements of "giant, obnoxious, and annoying" but there is an indicator of what portal you're signed into (or not signed into):

I can see I'm logged into one portal here:

And I know what org I'm signed into here:

And here:

Or with an enterprise sign-in:

And when I'm not signed in:

I underlined every single one, repeatedly, trying to turn up the obnoxious dial 

[ThomasColson]

I get the same user when logged into Portal and AGOL, and even with your screen shots, it's obvious that they're different, but still can't tell what you're logged into based on the user name, unless you can remember (which I can't). 

[KoryKramer]

Fair enough.

[JonahLay]

With ArcGIS Pro 3.0, your profile photo now displays in the application. While this may not meet the exact requirement request, adding a profile picture may help to differentiate between the different active portals.

[Waan]

Good recommendation. Esri, make it obvious--we shouldn't need to sift clues to see what we're logged into.