Is it correct to have nested Scaffold in Flutter?

I have a PageView in my app homepage and I want:

1. The AppBar changes according to the page
2. The BottomAppBar is fixed

The 2 solutions I imagined are:

1. The hard one: have one Scaffold with appBar, body and bottomNavigationBar; use the PageView's PageController to animate the AppBar content.
2. Have 2 nested Scaffold: the main one with body and bottomNavigationBar, and a second one in each PageView's page, with the AppBar.

So, I was wondering, it works, but is it "correct" syntactically to have nested Scaffolds?

Go here: https://api.flutter.dev/flutter/material/Scaffold-class.html

There is a section named Troubleshooting and inside it, you will find this:

Nested Scaffolds

The Scaffold was designed to be the single top level container for a MaterialApp and it's typically not necessary to nest scaffolds. For example in a tabbed UI, where the bottomNavigationBar is a TabBar and the body is a TabBarView, you might be tempted to make each tab bar view a scaffold with a differently titled AppBar. It would be better to add a listener to the TabController that updates the AppBar.