A Unity editor script which lets you save a Gradient as a texture file (place the script inside a folder named Editor).

GradientWindow.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEditor;
using System.IO;

public class GradientWindow : EditorWindow
{
    private Gradient gradient = new Gradient();
    private int resolution = 256;
    private string filename = "New Texture";
    private FileFormat format = FileFormat.PNG;

    [MenuItem("Window/Gradient2PNG", priority = 10000)]
    public static void ShowWindow()
    {
        GetWindow<GradientWindow>(false, "Gradient2PNG", true);
    }

    private void OnGUI()
    {
        EditorGUILayout.LabelField("Gradient to File Converter");
        gradient = EditorGUILayout.GradientField("Gradient", gradient);
        resolution = EditorGUILayout.IntField("Resolution", resolution);
        filename = EditorGUILayout.TextField("Filename", filename);
        format = (FileFormat)EditorGUILayout.EnumPopup("Format", format);

        GUILayout.FlexibleSpace();
        
        if(GUILayout.Button("Convert to asset", GUILayout.Height(50)))
        {
            ConvertGradient();
        }
    }

    private void ConvertGradient()
    {
        Texture2D tex = new Texture2D(resolution, 1);
        Color[] texColors = new Color[resolution];

        for(int x = 0; x < resolution; ++x)
        {
            texColors[x] = gradient.Evaluate((float)x / resolution);
        }

        tex.SetPixels(texColors);

        byte[] bytes = null;
        string filenameWithExtension = null;

        switch(format)
        {
            case FileFormat.JPG:
                bytes = tex.EncodeToJPG();
                filenameWithExtension = "/" + filename + ".jpg";
                break;
            case FileFormat.PNG:
                bytes = tex.EncodeToPNG();
                filenameWithExtension = "/" + filename + ".png";
                break;
            case FileFormat.TGA:
                bytes = tex.EncodeToTGA();
                filenameWithExtension = "/" + filename + ".tga";
                break;
        }

        try
        {
            string path = Application.dataPath + filenameWithExtension;

            var dir = Path.GetDirectoryName(path);
            if (!Directory.Exists(dir))
            {
                Directory.CreateDirectory(dir);
            }

            File.WriteAllBytes(path, bytes);
            AssetDatabase.Refresh();
        }
        catch(IOException e)
        {
            Debug.LogError(e);
        }
    }
}

public enum FileFormat
{
    JPG,
    PNG,
    TGA
}