Why would you run your text through an AI checker, ever? Why would you care what an AI checker has to say about anything you wrote? You know you wrote it. Isn't that enough? Don't understand at all.
Back to the topic. Emdashes.
Proper usage? That's tricky. If you need to think that hard about a justification for them, leave them out. Many novelists do. I've said above that they should augment established grammar and style, not replace established usage. And certainly they should never be "sprinkled in." They either serve some functional purpose, or they don't.
As to what is meant by augmenting grammar, it's helpful for sake of example to point post-secondary students to fine poetry. The best poets construct their own internally consistent alternate grammars. For instance, consider the poetry of e.e. cummings. His books establish consistent alternative systems that carry through entire volumes. He turns capitalization and punctuation rules inside out and upside-down, but there is an internal consistency to his systems. Other poets that are adept at effectively changing the rules include Berryman (Dream Songs), Duncan (Passages), Corman, (Of), and Ferlinghetti (Coney Island of the Mind, Wild Dreams of a New Beginning, etc.). And so many others. Fine poetry is where the rules are made and remade. Poetry is on the bleeding edge of the language and always has been.
Anyhoo, I can't tell you how to use emdashes. I can only tell you how I use them. When I do. Which is not always. For the stuff I'm posting now, I use them. Readers don't notice. They fit, and they flow. Consistency and purpose are the keys. My rules:
Endashes within sentences, and emdashes outside of sentences. (Though on websites like this I just use emdashes, sites don't render correctly and it becomes an editing nightmare to vary them.)
Usage, General Rule: emdashes delimit interruptions to narrative flow.
Emdashes in dialogue:
Emdashes at the end of monologues, when characters interrupt each other. In the example below, the first speaker never finishes her thought, so the sentence never ends.
"Last night my house burned down, and then"--
"Oh my god, was anyone hurt?"
Endashes within a monologue, when a character interrupts herself, effectively creating an embedded aside:
"Last night my house burned down-- how the air fryer caught fire is a long story-- and then...."
These usages attempt to mimic the non-linear and disjointed way that individuals naturally talk, and also the way groups tend to interrupt each other and jump erratically from topic to topic.
Emdashes in exposition:
I also use emdashes when the narrator interrupts herself, to qualify a scene or to elucidate the thought process of a character. There are two ways I use this, and both are forms of interruption. In one, the character interrupts her own thought process:
She loved him unconditionally and would not renege on her agreement to meet him again-- though in her more sober moments she questioned her sanity-- but she did have two more days to establish some boundaries and conditions.
I try to use this sparingly. If the characters are sufficiently developed and the scenes sufficiently foregrounded, it's often unnecessary, as there are better ways to interleave two threads of thought without the jarring effect of the interruption.
Another form of expositional interruption that I sometimes employ is the use of emdashes to mark interruption of the narrative by the author herself. This I do occasionally, though it is very rare.
She loved him unconditionally-- truly, there is no accounting for taste-- despite her palpable fear for her safety in his presence.
This use of an embedded aside can be a strong dramatic effect-- an opportunity for the author to editorialize on her own work-- but it must be extremely rare, or it becomes irritating.
And that's pretty much it. That's how I'm using emdashes these days. Interruptions to narrative flow, in various forms. These forms of usage fit the material, and I haven't had any complaints.
As to whether or not and in what manner emdashes fit in your own story-- if at all-- only you can decide. Purpose and consistency. Or not. :)