An approximation of Flutter's [Theme] implementation, demonstrating simple [InheritedWidget] use.

my_theme.dart

class MyThemeProvider extends StatefulWidget {
  const MyThemeProvider({Key? key, required this.child}) : super(key: key);

  final Widget child;

  @override
  State<MyThemeProvider> createState() => _MyThemeProviderState();
}

class _MyThemeProviderState extends State<MyThemeProvider> {
  var data = const MyThemeData();

  @override
  Widget build(BuildContext context) {
    return MyTheme(
      data: data,
      child: widget.child,
    );
  }
}

class MyTheme extends InheritedWidget {
  const MyTheme({
    Key? key,
    required this.data,
    required Widget child,
  }) : super(key: key, child: child);

  final MyThemeData data;

  @override
  bool updateShouldNotify(covariant MyTheme oldWidget) => false;

  static MyThemeData of(BuildContext context) {
    final result = context.dependOnInheritedWidgetOfExactType<MyTheme>();
    assert(result != null, 'No MyTheme in current BuildContext.');
    return result!.data;
  }
}

@immutable
class MyThemeData {
  const MyThemeData({
    this.backgroundColor = Colors.white,
    this.primaryColor = Colors.blue,
    this.textColor = Colors.black87,
  });

  final Color backgroundColor;
  final Color primaryColor;
  final Color textColor;

  MyThemeData copyWith({
    Color? backgroundColor,
    Color? primaryColor,
    Color? textColor,
  }) {
    return MyThemeData(
      backgroundColor: backgroundColor ?? this.backgroundColor,
      primaryColor: primaryColor ?? this.primaryColor,
      textColor: textColor ?? this.textColor,
    );
  }
}