AnimatedDefaultTextStyle

AnimatedContainer(
      duration: const Duration(milliseconds: 500),
      padding: const EdgeInsets.symmetric(vertical: Sizes.size16),
      decoration: BoxDecoration(
        borderRadius: BorderRadius.circular(Sizes.size5),
        color: disabled
            ? Colors.grey.shade300
            : Theme.of(context).primaryColor,
      ),
      child: AnimatedDefaultTextStyle(
        duration: const Duration(milliseconds: 500),
        style: TextStyle(
          color: disabled ? Colors.grey.shade400 : Colors.white,
          fontSize: Sizes.size16,
          fontWeight: FontWeight.w600,
        ),
        child: Text(
          text,
          textAlign: TextAlign.center,
        ),
      ),
    ),

다음과 같이 Text 위젯 바깥에 AnimatedDefaultTextStyle 위젯으로 감싼 다음 TextStyle을 바깥으로 옮기면 된다.