AutoSpriteSlicer.cs

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

// This is only useful for spritesheets that need to be automatically sliced (Sprite Editor > Slice > Automatic)
public class AutoSpriteSlicer
{
	[MenuItem("Tools/Slice Spritesheets %&s")]
	public static void Slice()
	{
		var textures = Selection.GetFiltered<Texture2D>(SelectionMode.Assets);

		foreach (var texture in textures)
		{
			ProcessTexture(texture);
		}
	}

	static void ProcessTexture(Texture2D texture)
	{
		string path = AssetDatabase.GetAssetPath(texture);
		var importer = AssetImporter.GetAtPath(path) as TextureImporter;

		//importer.isReadable = true;
		importer.textureType = TextureImporterType.Sprite;
		importer.spriteImportMode = SpriteImportMode.Multiple;
		importer.mipmapEnabled = false;
		importer.filterMode = FilterMode.Point;
		importer.spritePivot = Vector2.down;
		importer.textureCompression = TextureImporterCompression.Uncompressed;

		var textureSettings = new TextureImporterSettings(); // need this stupid class because spriteExtrude and spriteMeshType aren't exposed on TextureImporter
		importer.ReadTextureSettings(textureSettings);
		textureSettings.spriteMeshType = SpriteMeshType.Tight;
		textureSettings.spriteExtrude = 0;

		importer.SetTextureSettings(textureSettings);

		int minimumSpriteSize = 16;
		int extrudeSize = 0;

		Rect[] rects = InternalSpriteUtility.GenerateAutomaticSpriteRectangles(texture, minimumSpriteSize, extrudeSize);
		var rectsList = new List<Rect>(rects);
		rectsList = SortRects(rectsList, texture.width);

		string filenameNoExtension = Path.GetFileNameWithoutExtension(path);
		var metas = new List<SpriteMetaData>();
		int rectNum = 0;

		foreach (Rect rect in rectsList)
		{
			var meta = new SpriteMetaData();
			meta.pivot = Vector2.down; 
			meta.alignment = (int)SpriteAlignment.BottomCenter;
			meta.rect = rect;
			meta.name = filenameNoExtension + "_" + rectNum++;
			metas.Add(meta);
		}

		importer.spritesheet = metas.ToArray();

		AssetDatabase.ImportAsset(path, ImportAssetOptions.ForceUpdate);
	}

	static List<Rect> SortRects(List<Rect> rects, float textureWidth)
	{
		List<Rect> list = new List<Rect>();
		while (rects.Count > 0)
		{
			Rect rect = rects[rects.Count - 1];
			Rect sweepRect = new Rect(0f, rect.yMin, textureWidth, rect.height);
			List<Rect> list2 = RectSweep(rects, sweepRect);
			if (list2.Count <= 0)
			{
				list.AddRange(rects);
				break;
			}
			list.AddRange(list2);
		}
		return list;
	}

	static List<Rect> RectSweep(List<Rect> rects, Rect sweepRect)
	{
		List<Rect> result;
		if (rects == null || rects.Count == 0)
		{
			result = new List<Rect>();
		}
		else
		{
			List<Rect> list = new List<Rect>();
			foreach (Rect current in rects)
			{
				if (current.Overlaps(sweepRect))
				{
					list.Add(current);
				}
			}
			foreach (Rect current2 in list)
			{
				rects.Remove(current2);
			}
			list.Sort((a, b) => a.x.CompareTo(b.x));
			result = list;
		}
		return result;
	}
}

@shadesbelow Are you author of this code? Can you maybe specify license for it? Either by posting in comments here and for example declaring "It is MIT licensed" or by editing the code?

See https://choosealicense.com/

Editing TextureImporter.spritesheet no longer works in Unity 2020+
I shared a code snippet here (https://forum.unity.com/threads/sprite-editor-automatic-slicing-by-script.320776/#post-9756150) that works in newer versions of unity.