accessibility – Is an aria-label needed on icon fonts with additional context?

The icon is there to draw attention to the label, this is not a label in itself. The label should speak for itself and does not need an aria-label attribute.

To quote

If the text of the label is visible on the screen, the authors SHOULD use aria-labelledby and SHOULD NOT use aria-label.

So, instead of aria-label, you can do something like:

    Please, put a valid email address.

But I do not think you need to add aria-labelby to the icon because it has no special meaning on the label. It is clearly a matter of drawing attention to the etiquette of people who can see and who should be ignored by screen readers.
To make form validation more accessible, you can add an aria-invalid attribute to the entry:

Aria attributes should only be used if they are relevant and are used here
draw attention to invalid input for screen readers, just like the icon for people who depend on their eyes to scan the page.