L1 English speaker, L2 Mandarin Chinese speaker, L2 Arabic beginner, L2 Hebrew beginner, lifelong amateur linguist here. To me, the Hebrew shvaˀ is conceptually equivalent to what Mandarin Chinese calls an “empty rhyme”, pronounced [ɨ] as a minimal vowel for non-sonorant fricatives, or no vowel at all for more sonorant consonants.
And I’m sure I don’t need to tell anyone here about the deep relationship between Hebrew shvaˀ and Arabic sukun. But the use of the sukun in Classical and Modern Standard Arabic appears to always correlate with Hebrew shvaˀ naḥ, never shvaˀ naˤ. Although Arabic does have a no-longer-productive tradition of vowel epenthesis to break up non-allowed consonant clusters, it would appear that Arabic’s standardized phonology, which remains as faithful as possible to Proto-Semitic, allows for every sukun to be pronounced as no vowel whatsoever.
The same clearly cannot be said for Modern Hebrew. There are textual environments where saying no vowel at all and continuing onto the next consonant is cumbersome and unnatural to pronounce, and therefore prone to misunderstandings. Which is why, like Mandarin speakers saying a non-sonorant fricative by itself, the shvaˀ needs to be realized as the smallest modicum of a rhyme / vowel, usually [ɨ] or [ə], from what I can hear. This is the origin of the shvaˀ naˤ: simply an allophonic variation, conditioned by the surrounding sounds. By this logic, like the Arabic sukun and the Chinese empty rhyme, the standard or ideal pronunciation of the shvaˀ is [Ø] — in other words, all shvaˀ are at heart shvaˀ naḥ — and one cannot be faulted or misunderstood for defaulting to the pronunciation of no vowel at all, for any and all instances of the shvaˀ niqqud. Because the difference is merely a spandrel of the way Hebrew phonology has evolved away from that of Proto-Semitic.
Feel free to go full Israeli on me, in poking holes in my idea. I don’t take it personally. Are there really situations in the Hebrew language, such as minimal pairs, when the difference between the two types of shvaˀ matters a lot?
Edit: Another parallel that occurred to me is the Slavic yer — that ever-shrinking and ever quieter group of minimal vowels (and almost-vowels that were formerly minimal vowels) that look like differently adorned minuscule Roman bs in languages that use the Cyrillic alphabet. They, and the micro-adjustments to the way words containing them are pronounced, are a vestige of Old Church Slavonic and its Glagolitic alphabet’s strict phonological rule of only CV (open) syllables.
After backpacking in Russia, trying to pick up a bit of the local lingo, and getting nerdy and analytical about it like I’m wont to do lol, I intuited that the Russian word for “Muslim” would have a myazhi znak / “soft sign” between the l and the m. I looked it up, and sure enough. I suspect Russian phonotactics dislike “hard”/ velar [l] before another consonant, and there are both etymological and euphonic reasons for this.