I don't think it's currently possible to set a transparent value using a native HTML color input:
Note: Setting the value to anything that isn't a valid, fully-opaque, RGB color in hexadecimal notation will result in the value being set to #000000. In particular, you can't use CSS's standardized color names, or any CSS function syntax, to set the value.
This makes sense when you keep in mind that HTML and CSS are separate languages and specifications. In addition, colors with an alpha channel are not supported; specifying a color in 9-character hexadecimal notation (e.g. #009900aa) will also result in the color being set to #000000.
https://developer.mozilla.org/en-US/docs/Web/HTML/Element/input/color#value
A potential solution could be using a library like Pickr.js.