. . .that most of us have never thought about.

Thank you for shedding some light on this mostly hidden topic!

"an" orange, but "a" bowl. You don't think about it, you just say it that way.

With some differences by context.

But I must say, [ ən ] sounds utterly unnatural to me and /ə/ is disallowed in most standard English at least under stress (perhaps only primary stress). Maybe /_[n] matters and what you cite is a British variant (I remember by Czech students of English having a hellish time with /kænt/ which they insisted on pronouncing as [kɐnt] which was a rather bad error, as you can imagine. I imposed /kænt/ on them when they had trouble with [kɑ:nt]. Even [kɐ:nt] just came off as emphatic--even to Estuary and RCP speakers.

Also note how /n/ only occurs because of historically mis-parsing and generalization, not through n-insertion when /a/ was in hiatus with another /a/: "The apron" but "an apron" (*apron), or "the orange" v "an orange" (*narange or thereabouts, cf. Sp. naranja) and probably some Latin or Greek borrowings, me thinks. There's nothing like that for < the >.

Now /æn/ is generalized to /_# æ, where # is a morpheme boundary and [ən] ~ [æn] are in complementary distribution when unstressed, at least in every dialect of American (and British) English that I'm familiar with. But what do I know?