Is this maybe a thing like how only designers are aware of kerning? These read / sound very different to me, and to everyone I've brought up the subject with (who admittedly are in a certain bubble of people who either write professionally, or "do things" with their voices, or both.)
• The length of the verbal pause is different. (It's hard to quantify this, as it's relative to your speaking rate, which can fluctuate even within a sentence. But I can maybe describe it in terms of meter in poetry/songwriting: when allowed to, a parenthetical pause may be read to act as a one-syllable rest in the meter of a poem, often helpfully shifting the words in the parenthetical over to properly end-align a pair of rhyming [but otherwise misaligned] feet. An em-dash, on the other hand, acts as only a half-syllable rest; it therefore offsets the meter of the words in the subclause that follow, until the closing em-dash adds another half-syllable rest to set things right. This is in part why ChatGPT's favored sentences, consisting of "peer" clauses joined by a single em-dash, are somewhat grating to mentally read aloud; you end up "off" by a half-syllable after them, unless you can read ahead far enough to notice that there's no closing em-dash in the sentence, and so allow the em-dash-length pause to read as a semicolon-length pause instead.)
• The voicing of the last word before the opening parenthesis / first em-dash starts is different. (paren = slow down for last few words before the paren, then suddenly speed up, and override the word's normal tonal emphasis with a last-syllable-emphasized rising tone + de-voicing of vowels; em-dash = slow down and over-enunciate last few words before the em-dash, then read the last syllable before the em-dash louder with a overridden falling voiced tone)
• The speed at which, and vocal register with which, the aside / subclause is read is different. (parens = lowest register you can comfortably speak at, slightly quieter, slightly faster than you were delivering the toplevel sentence; em-dashes = delivery same speed or slower, first few syllables given overridden voiced emphasis with rising tone from low to normal, and last few syllables given overridden voiced emphasis with falling tone from normal to low)
• The voicing of the first words after the subclause ends is different. (closing paren = resume speaking precisely as if the parenthetical didn't happen; second em-dash = give a fast, flat-low nasally voiced performance of the first one or two syllables after the em-dash.)
To describe the overall effect of these tweaks:
A parenthetical should be heard as if embedded into the sentence very deliberately, but delivered as an aside / tangent, smaller and off-to-the-side, almost an "inlined footnote", trying to not distract from the point, nor to "blow the listener's stack" by losing the thread of the toplevel point in considering it.
An em-dash-enclosed interruptive subclause should read like the speaker has realized at the last moment that they have two related points to make; that they are seemingly proceeding, after a stutter, to finish the sentence with the subclause; but that they are then "backing up" and finishing the same sentence again with the toplevel clause. The verbalization should be able to be visualized as the outer sentence being "squashed in" to "make room" for the interruptive subclause; and the interruptive subclause "squashing at the edges" [tonally up or down, though usually down] to indicate its own "squeezed in" beginning and end edges.
Note that this isn't subjective/anecdotal descriptions from how I speak myself. These are actually my attempt to distill vocal coaching guidelines I've learned for:
• live sight-reading of teleprompter lines containing these elements, as a TV show host / news anchor
• default-assumed directorial expectations for lines containing elements like these, when giving screenplay readings as a [voice] actor (before any directorial "notes" come into play)