Can I use
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Drag and Drop

- LS

Method of easily dragging and dropping elements on a page, requiring minimal JavaScript.

Chrome

  1. ✅ 4 - 133: Supported
  2. ✅ 134: Supported
  3. ✅ 135 - 137: Supported

Edge

  1. ◐ 12 - 17: Partial support
  2. ✅ 18 - 133: Supported
  3. ✅ 134: Supported

Safari

  1. ✅ 3.1 - 18.2: Supported
  2. ✅ 18.3: Supported
  3. ✅ 18.4 - TP: Supported

Firefox

  1. ❌ 2 - 3: Not supported (but has polyfill available)
  2. ✅ 3.5 - 135: Supported
  3. ✅ 136: Supported
  4. ✅ 137 - 139: Supported

Opera

  1. ❌ 9 - 11.6: Not supported (but has polyfill available)
  2. ✅ 12 - 116: Supported
  3. ✅ 117: Supported

IE

  1. ◐ 5.5 - 9: Partial support
  2. ◐ 10: Partial support
  3. ◐ 11: Partial support

Chrome for Android

  1. ✅ 134: Supported

Safari on iOS

  1. ❌ 3.2 - 14.8: Not supported
  2. ✅ 15 - 18.2: Supported
  3. ✅ 18.3: Supported
  4. ✅ 18.4: Supported

Samsung Internet

  1. ❌ 4 - 26: Not supported
  2. ❌ 27: Not supported

Opera Mini

  1. ❌ all: Not supported

Opera Mobile

  1. ❌ 10 - 12: Not supported (but has polyfill available)
  2. ✅ 12.1: Supported
  3. ✅ 80: Supported

UC Browser for Android

  1. ✅ 15.5: Supported

Android Browser

  1. ❌ 2.1 - 4.4.4: Not supported
  2. ✅ 134: Supported

Firefox for Android

  1. ❌ 136: Not supported

QQ Browser

  1. ✅ 14.9: Supported

Baidu Browser

  1. ❌ 13.52: Not supported

KaiOS Browser

  1. ❌ 2.5: Not supported
  2. ❌ 3: Not supported

dataTransfer.items only supported by Chrome.

Currently no browser supports the dropzone attribute.

Firefox supports any kind of DOM elements for .setDragImage. Chrome must have either an HTMLImageElement or any kind of DOM Element attached to the DOM and within the viewport of the browser for .setDragImage.

Resources:
Polyfill for setDragImage in IE
iOS/Android shim for HTML 5 drag'n'drop
HTML5 Doctor article
Shopping cart demo
WebPlatform Docs