I suggest also to add those:

• webkit-datetime-edit-year-field
• webkit-datetime-edit-month-field
• webkit-datetime-edit-day-field

https://jsfiddle.net/y8fbcvL6/1/

Would be great to have this added!
Since Firefox >= 109 there is visual issue that you can't hide date picker icon, i.e. following is not working anymore:

input[type="date"]::-webkit-calendar-picker-indicator {
    background: none;
}

So browser compatibility transparency is important!

Here is the recent test: https://codesandbox.io/s/webkit-calendar-picker-indicator-6lpfb9

Reference to Firefox bug: https://bugzilla.mozilla.org/show_bug.cgi?id=1812397