iOS 13 App Store update missing from the Account panel
It turns out that the update section doesn't appear in the account list at all until an update is available or has been automatically applied.  Any updates applied on the prior phone with the older iOS don't show in the list.  

I had hoped to figure all this out right away when I was doing the phone change so I would know that the phone transfer had worked successfully.  (I initially feared that the transfer had partially failed and that I wouldn't be able to do updates on the new phone.)  But I ended up needing to wait for an app to need an upgrade to get my answer for sure.  So hopefully this question and answer will help somebody else who is going through that to know that the transfer worked out fine and not to worry about that.