Q:

Connect separate lists in HTML for assistive technology

In my HTML, I have a description list which I had to split up for presentational purposes.
Let's assume the following HTML:
<div class="styling-1">
  <dl id="list-1">
    <dt>Item 1</dt>
    <dd>Description 1</dd>

    <dt>Item 2</dt>
    <dd>Description 2</dd>
  </dl>
</div>
<div class="styling-2">
  <dl id="list-2">
    <dt>Item 3</dt>
    <dd>Description 3</dd>

    <dt>Item 4</dt>
    <dd>Description 4</dd>
  </dl>
</div>

EDIT: Side note for clarification: I cannot use a CSS grid, column layout, ... to take one semantic list and adjust the distribution of its items. The lists are required to be kept separate in HTML.

Now macOS' VoiceOver naturally announces this as two description lists. This is not a deal breaker, but since they are — semantically — a single list, it would be better to have them announced as one.
Hence my question: Does WAI-ARIA (or any other declarative tool) offer a way to tell assistive technology that list-2 is a continuation of list-1?

A:

Now macOS' VoiceOver naturally announces this as two description lists. This is not a deal breaker, but since they are — semantically — a single list, it would be better to have them announced as one.

You're approaching the problem the wrong way round IMHO. The display of your document shouldn't dictate its semantic.
If both lists should be in one single list then do that and find a way to "separate" them on the screen.
According to MDN, it's ok to wrap <dt>, <dd> pairs in <div>:

WHATWG HTML allows wrapping each name-value group in a  element in a  element. This can be useful when using microdata, or when global attributes apply to a whole group, or for styling purposes.

<dl>
  <div>
    <dt>Name</dt>
    <dd>Godzilla</dd>
  </div>
  <div>
    <dt>Born</dt>
    <dd>1952</dd>
  </div>
  <div>
    <dt>Birthplace</dt>
    <dd>Japan</dd>
  </div>
  <div>
    <dt>Color</dt>
    <dd>Green</dd>
  </div>
</dl>

So you should be able to "break" this single list into two:
<dl>
  <div>
    <dt>Name</dt>
    <dd>Godzilla</dd>
  </div>
  <div>
    <dt>Born</dt>
    <dd>1952</dd>
  </div>
  <div class="new-column">
    <dt>Birthplace</dt>
    <dd>Japan</dd>
  </div>
  <div>
    <dt>Color</dt>
    <dd>Green</dd>
  </div>
</dl>

