But it leaves me worried that $_ is being used in say() as a global...

That's what $_ is; a global; and it's exactly what the real say does, along with a raft of other built-ins.

But it's a read-only reference, so it cannot harm anything.

So the question is, is that $_ referenced in the say() sub a global from the implicit $_ in the mainline loop, or not...?

I cannot parse the highlighted bit of that sentence.

Perhaps this will satisfy: There is only one $_ at any given time. It is the global $_.

Sometimes it is localised implicitely by some constructs (eg. for, while) and sometimes explicitly by user code; but all that means is that a copy of the previous value is kept somewhere and gets restored once the localisation ends.

Whenever you use $_; you get its current value, regardless of whether it has been localised in one or many previous scopes.