How can I use a different locale than the one defined for the whole Flutter app in one part of it? 

Overriding the inherited locale and localizations delegates for a child widget is pretty easy in Flutter.
For that purpose, you only need to wrap the desired widget with the Localizations.override factory constructor.

class OtherLocalized extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Localizations.override(
      context: context,
      locale: const Locale("es"),
      child: Builder(
        builder: (BuildContext context) => Center(
          child: Text(
            AppLocalizations.of(context)!.textIntroFirstPageTitle,
          ),
        },
      ),
    );
  }
}

Flutter internationalization tutorial:

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