Following the newer definition, the aside element should be inside of the section element to which it is related. The main element is not a sectioning element (elements like article, section, body, figure etc. are). You can of course still place aside in main, but it will be related to the nearest sectioning element parent of main. That means there is no semantic difference (for aside) in these two examples:

Regarding the first example, we have to put aside the fact that we (from inspection) can see the runtime behavior of this code by executing it in our heads.

CSS-generated content is not included in the DOM. Because of this, it will not be represented in the accessibility tree and certain assistive technology/browser combinations will not announce it. If the content conveys information that is critical to understanding the page's purpose, it is better to include it in the main document.

<aside> is appropriate if the side note "could be considered separate from the content"

<aside> is not appropriate if the side note is "a parenthetical". The W3C gives no examples of what it means.

In my opinion, the W3C definition is unnecessarily confusing and restrictive. The dictionary definition of aside is "a temporary departure from a main theme or topic", and the spec should just stick to that, rather than introducing subtle distinctions.

The dictionary definition of aside is "a temporary departure from a main theme or topic"

a temporary departure from a main theme or topic; brief digression.

A temporary departure from a main theme or topic, esp. a parenthetical comment or remark; short digression.

(of a subject or activity) different than the one you are talking about or doing: a tangential issue

Tangentially is defined as briefly mentioning a subject but not going into it in detail, or is defined as going off in a different direction.

1a : touching lightly : incidental, peripheral tangential involvement also : of little relevance arguments tangential to the main point

The informative asides about rural life make this wine guide rather special.

a remark or story in a speech or text that is not part of the main subject:

He frequently interrupted his narrative with amusing asides.

a comment or discussion that does not relate directly to the main subject being discussed : digression