Start doing it for money, and you're officially a professional software engineer.
Make software that genuinely improves peoples lives (like the Linux kernel currently running the computer I'm typing these words on), and you can call yourself a good software engineer ^_^
But I too have met engineers with music and also medical backgrounds. But that's all more than half a century ago, it seems that employers expect much more narrowly focussed qualifications these days.
Just like writing favorite instead of favourite, while I'm here, I think the right thing to do is respect the customs of the country which welcomed me. It would be very ignorant of me to pretend I'm more of an engineer than my American colleagues with CS degrees.
Afaik claiming to have an MD (for obvious reasons) or a PhD would land you in hot water much, much faster, despite technically being exactly the same "offense"
I think it's fine.
That doesn’t mean that certain professional engineering disciplines exist that are regulated in the US. Systems Engineer, Computer Enginner, etc are not in that realm.
In the US, engineering is regulated only where public safety is directly at stake. Most engineers work for companies that assume liability for their work.