It appears the issue may only occur with orders that were archived (There are instances here where users have ‘archived’ orders and then ‘unarchived’ them).
In these cases, it seems to make a difference what format is used when specifying the “created_at_min” timestamp in the search query.
The following timestamp formats did not work for me:
“…orders.json?status=any&created_at_min=2021-09-20T04:00:00”, (This should default to the shop’s native time zone, but appears not to) or
“…orders.json?status=any&created_at_min=2021-09-20T04:00:00__+09:30__” (The Shop’s UTC offset included)
However, I know a plus (+) character in a URL is interpreted as a space character, so following a suggestion in another message, I URL encoded the time zone string, which worked!