How to center a column in the appbar

how do I Center a column in the Appbar? I've searched online and even after adding a row with mainAxisAlignment and mainAxisSize, the Column is still not centered. TIA for all inputs. Additionally, the page is a second page, hence, there is a leading icon.

return Scaffold(
      appBar: AppBar(
        centerTitle: true,
        title: Container(
          color: Colors.deepPurple,
          child: Row(
            mainAxisAlignment: MainAxisAlignment.center,
            mainAxisSize: MainAxisSize.min,
            children: [
              Column(
                children: [
                  Padding(
                    padding: const EdgeInsets.only(top: 8.0),
                    child: Text(widget.id),
                  ),
                  Padding(
                    padding: const EdgeInsets.symmetric(vertical: 8.0),
                    child: Text(
                      _caption,
                      style: const TextStyle(fontSize: 14),
                    ),
                  ),
                ],
              ),
            ],
          ),
        ),
      ),
    );

You code works as intended:

Look how your widget appears: it correctly centers the column inside the AppBar.

And here's a little example that centers a column within app bar, it's all about setting centerTitle: true,

appBar: AppBar(
  backgroundColor: Colors.blue,
  centerTitle: true,
  title: Column(
    children: [
      Text('First Text'),
      Text('Second Text'),
      
    ],
  ),

How it looks:

If you are expecting a different output, just let me know.

Updates

Now, The leading widget is in the center calculations, we must ignore it from calculation, which can be done by setting a similar widget that allocate the same width as leading in actions of the appbar:

  appBar: AppBar(
    title: Container(
      color: Colors.amber,
      child: Column(
        children: [
          Text('Centered Centered'),Text('Centered'),
        ],
      ),
    ),
    centerTitle: true,
    leadingWidth: 60,
    leading: GestureDetector(
      child: Icon(Icons.arrow_back),
    ) ,
    actions: [
      SizedBox(width: 60,),
    ],
  ),

which appears like this, it's totally centered:

Hope it helps you.