Parenthesis

Parenthesis is the insertion of an aside into a sentence that is grammatically complete without it, marked off by commas, dashes or brackets, so the reader hears a second voice cutting across the first.

The estimate (which nobody had checked) went out on the Friday.

Lift the aside and the sentence is intact. That is the test, and it is what separates a parenthesis from a bound modifier, which cannot be lifted.

The three punctuations are not interchangeable. They are a volume control.

• Commas — quietest. The aside stays inside the sentence: The estimate, unchecked, went out on the Friday.
• Dashes — loudest. The aside interrupts, and the reader hears an emphasis: The estimate — unchecked, of course — went out on the Friday.
• Round brackets — the most detached. The aside is muttered aside from the sentence rather than into it: The estimate (unchecked) went out on the Friday.

In first-person narration the bracketed aside is a characterisation device in its own right, because it establishes a narrator who is editing themselves in front of you, and a narrator who does that is a narrator with something to manage.

Two limits. A parenthesis that runs long enough to make the reader lose the main clause has failed, whatever the brackets say — see mid-sentence modifier. And more than one per paragraph starts to read as a nervous habit rather than a voice.