Positioned Widget is not scrolling even with all positional arguments

You will be fine if you just wrap your container inside a SingleChildScrollView

The child widget inherits constraints from the parent. I added a parent container with height: double.infinity. Also the segment_two container I set a minimum height of 150 otherwise you will give pixel overflow. Be careful with your ratios on sizing.

class TestPositioned extends StatefulWidget {
  TestPositioned({Key? key}) : super(key: key);
  @override
  State<TestPositioned> createState() => _TestPositionedState();
}
class _TestPositionedState extends State<TestPositioned> {
  segment_one(BuildContext context)
  {
          return Container(
            width: MediaQuery.of(context).size.width * 1,
            height: MediaQuery.of(context).size.height * .35,
            decoration: BoxDecoration(
              border:Border.all(color:Colors.grey)),
              child:FittedBox(
                fit:BoxFit.fitHeight,
              child:SizedBox(
                width:200,
                height:200,
                child: Image.asset("assets/images/apple.jpg"),
              ),
            ),
          );
  }
  segment_two(BuildContext context)
  {
    return 
          Positioned(
            bottom: -MediaQuery.of(context).size.height * 0.01,
            child: 
            
            Container(
                width: MediaQuery.of(context).size.width * 1,
                height: MediaQuery.of(context).size.height * 0.26>150?MediaQuery.of(context).size.height * 0.26:150,
                
                  child:Card(
                      color: Colors.teal.shade50,
                      shape: RoundedRectangleBorder(
                          borderRadius: BorderRadius.only(
                          topLeft: Radius.circular(40),
                          topRight: Radius.circular(40),
                  )),
                  elevation: 0,
                       child: Column(
                      children: [
                            Expanded(child:Text("full Name", style: TextStyle( fontWeight: FontWeight.bold, fontSize: 24, ),)),
                            Expanded(child:Text("current age" + " name",style: TextStyle(fontSize: 22,))),
                            Expanded(child:Text('abcdefg: hijklmn',style: TextStyle(color: Colors.grey,fontSize: 16,))),
                            SizedBox(height: 10,),
                            
                            Container(margin: EdgeInsets.symmetric(horizontal: 10),
                              padding:EdgeInsets.symmetric(horizontal: 10, vertical: 5),
                              child: 
                              Expanded(child:Text("bio",maxLines: 3,overflow: TextOverflow.ellipsis,textAlign: TextAlign.center,
                              style: TextStyle( fontSize: 20,)))
                              )
                              ,
                            SizedBox(height: 10,),
                  ],
                ),
              )));

  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(appBar: AppBar(title: Text("Stacked Position")),body:
    Container(
          height: double.infinity,child:Stack(
      children: [
      segment_one(context),
      segment_two(context),
   ],)));
  }
}

I solved it, which took me quite a while but now it is working perfectly for my purposes. I am still using the stack but to push the content down to where it is needed, I used a transparent container. Now the MediaQuery isn't negative anymore. Might not be the perfect answer, but it works.

return Scaffold(
  backgroundColor: Colors.teal.shade50,
  appBar: AppBar(
    elevation: 2,
    leading: BackButton(onPressed: () {
      Navigator.pop(context,
          MaterialPageRoute(builder: (context) => eventHomeScreen()));
    }),
    backgroundColor: Colors.teal,
    title: Text('Leute', style: TextStyle(fontSize: 28)),
    actions: [
      IconButton(
        iconSize: 26,
        icon: Icon(Icons.chat),
        tooltip: 'Chat-Anfrage schicken',
        onPressed: () {
          Navigator.of(context).push(MaterialPageRoute(
              builder: (context) => chatRequestSentScreen.withUser(user)));
        },
      )
    ],
  ),
  body: Stack(
    children: [
      Column(children: <Widget>[
          Container(
            height: MediaQuery.of(context).size.height * .33,
            decoration: BoxDecoration(
              image: DecorationImage(
                image: user.getProfilePicture(),
                fit: BoxFit.cover,
              ),
            ),
          ),
        ]),
      Positioned(
        top: MediaQuery.of(context).size.height * .27,
        child: Container(
          decoration: BoxDecoration(
              color: Colors.teal.shade50,
              borderRadius: BorderRadius.only(
                topLeft: Radius.circular(40),
                topRight: Radius.circular(40),
              )),
          width: MediaQuery.of(context).size.width * 1,
          child: Column(
            children: [
              Text(
                user.getFullName(),
                style: TextStyle(
                  fontWeight: FontWeight.bold,
                  fontSize: 24,
                ),
              ),
              Text(user.getCurrentAge().toString() + " Jahre",
                  style: TextStyle(
                    fontSize: 22,
                  )),
              Text('Zuletzt aktiv: Heute',
                  style: TextStyle(
                    color: Colors.grey,
                    fontSize: 16,
                  )),
            ],
          ),
        ),
      ),
      SingleChildScrollView(
        physics: NeverScrollableScrollPhysics(),
        child: Column(
          children: [
            Container(
              height: MediaQuery.of(context).size.height * .39,
              color: Colors.transparent,
            ),
            Container(
              height: MediaQuery.of(context).size.height * .15,
              width: MediaQuery.of(context).size.width * 1,
              color: Colors.teal.shade50,
              padding: EdgeInsets.symmetric(horizontal: 15, vertical: 0),
              child: SingleChildScrollView(
                physics: AlwaysScrollableScrollPhysics(),
                child: Text(
                   user.getBio(),
                  textAlign: TextAlign.center,
                  style: TextStyle(
                    fontSize: 20,
                  ),
                ),
              ),
            ),
            Container(
              height: MediaQuery.of(context).size.height * .4,
              width: MediaQuery.of(context).size.width *1 ,
              decoration: BoxDecoration(
                  color: Colors.black87,
                  borderRadius: BorderRadius.only(
                    topLeft: Radius.circular(40),
                    topRight: Radius.circular(40),
                  )),
              child: Container(
                margin: EdgeInsets.symmetric(horizontal: 20, vertical: 0),
                padding: EdgeInsets.symmetric(horizontal: 10, vertical: 20),
                child: SingleChildScrollView(
                  physics: AlwaysScrollableScrollPhysics(),
                  child: Column(
                    children:
                        SharedScreenFeatures.getSports(user.getSports()),
                  ),
                ),
              ),
            ),
          ],
        ),
      ),
    ],
  ),
);