Unity uses X=right/left, Y=up/down, and Z=forward/back but these are, as you say conventions. Even within the engines themselves things like samples and tutorials will be laid out with these conventions and yet a simple rotation means you can have your game use whichever layout you want. The reality is that, no, there is no accepted “standard” since axes labels are arbitrary anyway. The labels of XYZ themselves are just a convention.
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