Is it well-defined where the approach segment begins when you're
vectored for SHN NDB-A?

Yes, in theory. ;-) You're on the final approach segment where the
initial segment intersects the final approach course at (or within)
the 10 nm limit stated in the chart.

How you would detect this on a vectors to final outside this limit is
point of the original poster. I never waste NDB approaches by doing
vectors to final, so I haven't given any thought to the issue. ATC
probably ought not to do what they did, but I'm not aware of any rules
stating such.