At least with regard to the second instance that the poster asks about—
What a pain, I wish I were NEETing it up at home— Hm, that's exciting. I think I have some inspiration now.
—The Chicago Manual of Style, sixteenth edition (2010) does provide relevant guidance, although it does so rather indirectly. In the poster's example, the interjection "hm" is a pause-to-reflect speech marker, not a syntactical element per se. If we remove it from consideration temporarily, we have this construction:
What a pain, I wish I were NEETing it up at home— that's exciting. I think I have some inspiration now.
Section 6.83 of Chicago addresses this type of construction:
6.83 Em dash between noun and pronoun. An em dash is occasionally used to set off an introductory noun, or a series of nouns from a pronoun that introduces the main clause.
Consensus—that was the will-o'the-wisp he doggedly pursued.
Broken promises, petty rivalries, and false rumors—such were the obstacles he encountered.
Darkness, thunder, a sudden scream—nothing alarmed the child.
Kingston, who first conceived the idea; Barber, who organized the fundraising campaign; and West, who conducted the investigation—those were the women who were responsible for the movement's early success.
Viewing the poster's second example as a member of this family of constructions in which a pronoun follows one or more nouns and "introduces the main clause," we might fit the example into the same punctuation framework as follows:
What a pain, I wish I were NEETing it up at home—that's an exciting thought. I think I have some inspiration now.
Or, restoring the temporizing 'hm':
What a pain, I wish I were NEETing it up at home—hm, that's an exciting thought. I think I have some inspiration now.
This construction will look odd to some readers because they more frequently see solitary (as opposed to paired) em dashes "used to indicate sudden breaks in thought or sentence structure or an interruption in dialogue," as Chicago section 6.84 puts it. Nevertheless, employing an em dash to link a pronoun that begins "the main clause" following an introductory noun, or series of nouns or entire thought is simply a different category of accepted (by Chicago) em dash use.
What section 6.83 of Chicago doesn't explicitly say—but clearly indicates in all of its included examples—is that (1) there should not be a letter space following the em dash, and (2) the initial word following the em dash should not be capitalized. In accordance with these implicit imperatives, if I were forced to retain the exact wording of the poster's example and the em dash, I would punctuate it as follows:
What a pain; I wish I were NEETing it up at home—hm, that's exciting. I think I have some inspiration now.
As for the poster's first example—
Naturally, I've already arranged for a backup plan to help those who have been overwhelmed by stress— Since the virtual sandbox is a simulated practice environment, you can leave from any area of it.
—I can't offer any justification for using an em dash instead of either a period or a colon to separate the two sentences/thoughts there.