There's a pretty well established definition:
https://en.wikipedia.org/wiki/Supernatural
> It sounds like you are using it to mean "a supernatural phenomena is one which cannot be explained by the current scientific models".
Yes, that's close enough.
> In this case, by definition the scientific method cannot support supernatural explanations.
Wrong, because in the first case you included the word "current" and in the second you didn't.
The reason that the supernatural is what it is today is because no observations require it as an explanation. But that could change at any time.
> I would argue that the vast majority of working scientists are naturalists - they accept something as being scientific only if it can be observed, measured, tested etc... .
The scientific method is to come up with the best explanation that accounts for all observations [1]. Things that are not observed need not be accounted for.
[1] https://blog.rongarret.info/2024/03/a-clean-sheet-introducti...
It sounds like you are using it to mean "a supernatural phenomena is one which cannot be explained by the current scientific models". In this case, by definition the scientific method cannot support supernatural explanations.
Some people might take "supernatural" to mean "beyond any possible scientific law of nature, full stop". But even here we have that by definition the scientific method cannot support supernatural explanations.
I would argue that the vast majority of working scientists are naturalists - they accept something as being scientific only if it can be observed, measured, tested etc... .