Assume we're not talking about nmap (since it's widely known as a hacker tool which may muddy the waters), but instead of a user-written program that e.g. checks for open ports. If a port is open to the public internet, what exactly makes a connection to it "unwarranted"?
As for the AWS rule, scanning open ports does not violate, by itself, any of those things.
Intent: What is the connection's purpose? To use a service, to map a topology, to identify potentially vulnerable targets, to consume resources?
Impact: How does the act of connecting (once or many times) affect the remote end of the connection? Is a critical resource being exhausted (network connections, cpu, memory, etc)? Is the remote end's service still available for its intended purpose?
There's no magic spot on the scales but the further you get away from "to use the service" on the Intent scale and "no detectable impact" on the Impact scale, the more trouble you're likely to run into.
You're looking for a line in the sand (for whatever reason) but no provider will give one, nor should they. Because that would mean telling attackers how to get close to the line without going over it.
I'm asking questions to widen my understanding of how and why I might get in trouble for it.
And I know, now you want to define "legitimate user traffic".
The problem is that the expectation for such strictly defined terms is what leads to legalese that's impossible for anyone that isn't a lawyer to understand.
Several years ago (so things may be different now), I snagged a free-tier (IIRC, it was free for six months or something like that) AWS instance specifically to battle-test my new firewall and config.
Within an hour of beginning tests, I received a notification from AWS asking me why I was doing port scans/etc. and that they wanted me to stop or I'd be kicked off.
I replied and documented that I was testing my own systems/networks and they backed off. I completed my testing and never heard anything from them after that.
Like I said, this was a few years ago (2019, I think), so things may be different now, but back then AWS was definitely proactive about this stuff.