is it really incorrect to refer to E♭ as D♯ if one mentions them
standalone with no reference to tonality?
If there's really "no reference to tonality," then the naming system is arbitrary, so E♭ and D♯ basically can be used interchangeably.
Perhaps an ascending chromatic scale has sharps and descending has
When simply writing out chromatic scales, this is often the convention used. Partly this is used because it avoids excessive accidentals (e.g., when ascending, one can write the natural form of a note and then the sharp, whereas if one wrote an ascending line using flats, the flat form would have to come first, then followed by a natural, requiring both a flat sign and a natural sign, instead of just one sharp for a similar passage -- you'd need about twice as many accidentals, including all the naturals, to write it the other way).
This desire for fewer accidentals can influence other notational choices, even outside of tonality. For example, if one were writing out a trill-like figure moving from D up a half step, it would be more efficient to write "D-E♭-D-E♭-D" etc. rather than writing a string of D-naturals and D-sharps one after each other. On the other hand, a neighbor tone before an E would be easier to write as a D♯ (i.e., E-D♯-E) for similar reasons.
The other issue is that even outside of tonality, sometimes a sharp or flat is preferred because of where the note leads to (or, less often, where it is coming from). Sharps generally lead up, while flats lead down.
And sometimes it's helpful to choose accidentals based on the context, often to show a familiar interval or chord, even in an atonal piece. For example, a leap from E♭ to A♯ can be hard to read, but write it as E♭ to B♭ and it can be easily identified as a perfect fifth. (This can be particularly helpful for singers and instruments that have flexible pitch, like many string instruments, to be able to make connections and see common intervals to sing/play in tune.) Similarly, if a chord is actually meant to sound like a major chord, it makes little sense to write it as D♯-G-B♭ rather than the more straightforward spelling as an E♭ chord.
That said, when working in a completely atonal context, some composers make arbitrary choices like using all sharps, regardless of context. That can give some consistency as well, at the occasional expense of inefficiency in situations like those discussed above.