How to launch Ubuntu Software Center from GNOME Shell?

So I think what you're alluding to is that although Gnome Shell presents a version of the "Applications" menu, it doesn't (AFAIK) present the "System" menu anywhere.

So, you have to still might want to add a launcher for the tool you want to run somewhere in the Applications menu tree. That's easy but not trivial:

1. Click on your name up in the upper right hand corner.
2. Click on System Preferences....
3. Click on "Main Menu" in the Look-and-Feel section of the "Control Center" that pops up.
4. Select the section where you want to add the software-center launcher - I chose "System tools".
5. Click the "new item" button.
6. Enter "software-center" as both the name and the command.
7. Click "OK".
8. Click "Close".

Now when you select "Activities" in the upper left hand corner, then the "more" button just to the right of the word "Applications", you'll see your new software-center launcher listed in the system tools menu.

I tried this and it worked perfectly.

EDIT: I don't know why I didn't see it there; it appears there's already a launcher for this; "Ubuntu Software Center" is a launcher in the "System" section of "System Preferences..." control center.

I haven't verified, but it looks to me like Gnome-Shell is presenting the Applications menu under that "more" button I mentioned above, and presenting the System menu within the control center that pops up when you choose "System Preferences..."

It didn't bring it back for me, but I Opened it, then in activities, right click and "Add to favourites", it's not with the rest of apps, but at least it's close and accessible