IMO for most text-fields and markdown interfaces it's a shortcode.
:smile: :calculator: :pikachu_brandishing_ketchup:
The only big downside to shortcodes are that they're more than one character long, but there's no good way I can think of to have screenreader-accessible emoji that doesn't contain a multiple-character description anyway.
Shortcodes will get passed properly through 99.9% of existing text processors without any problems, so it's a really safe format to store things in.
I think the conversion to pictorial form should only happen at the display layer. If you're writing HTML, I advocate for using an SVG with a title attribute. Unicode emoji are already SVGs, so the only thing that changes is you don't bundle your emoji into a font.
Even native applications understand how to automatically highlight things like urls with the `https://` `http://` format, so my personal vote is we just use shortcodes the same way we use URLs.