I did a quick ask around the office asking which order people would use when introducing themselves to someone from abroad. About half said "FamilyName GivenName", the other half said "GivenName FamilyName". So basically, if you meet someone from Japan the most straightforward thing to do is ask what they would prefer to be called.
[1]https://www.japantimes.co.jp/news/2019/09/06/national/japane...
I don't think Japanese people are in any state of confusion when they say Jack-san. Japanese people simply feel that dropping "san" would be rude and they have always been taught to refer to westerners by their given names. "san" doesn't exactly neatly map onto Mr either. Saying things like "driver-san" or "foreigner-san" is perfectly normal.
How rude is it to not use "san"? I've seen a client blow up over not having san attached to their name in an English email. Manners like this are quite deeply engrained: try not saying "thank you" the next time someone hands you something, it feels deeply wrong. It's hard to blame Japanese people for a similar adherence to manners.
They make it clear that whenever you use their given name you should NOT add "san" to it.
So that's kind of weird that they do it for foreigners.
Yes they add "-san" to pretty much anything, but their given name is the one notable exception.
I think that there are ancient roots of this, for example in the Heian era the fact to be in relationship with a girl was synonymous to know her given name, and use it to call her before the date ("yobai"). The given name in Japan is something very personal and private, and this would explain why it seems incongruous to them when it is used with "-san".
From my experience, when speaking in Japanese, they are quite strict (if you are not a customer of course, in this case they would hide their feeling) about not adding "-san" to their given name, when they allow you to use the bare given name.
In the story you relate, in this email in English, was it the given name that was used, or the family name?
https://www.npr.org/2019/05/22/725753561/shinzo-abe-or-abe-s...
Capitalizing the family name first is recommended here: https://www.languagemagazine.com/2020/01/23/japan-reverses-w...
I admit, it is confusing even for a Japanese speaker which one to me which is his family name or if I already need to flip the order.
The context is that too many people accidentally address him by his first name which is considered a bit embarrassing for polite society.