Python doesn't have automatic semicolon insertion.
Because of how good the rules are for Python's needs, most people never know that semicolons even exist in Python.
The two systems have in common that you can either include or omit a semicolon when you've got a simple statement on its own line, but under the hood they're different; the missing semicolon at the end of a line in idiomatic Python is not "automatically inserted by the parser", it is simply not needed at all. There are also behavioral differences; for example, in Go and JavaScript a semicolon on a line by itself is legal and does nothing, while in Python it's a syntax error.
Those "newline tokens" are effectively the equivalent to a semicolon in the parser. They are statement terminators. The way that Odin or Python handles them is effectively the same except when I tokenize the newlines, they are treated as semicolons but with the "text" being "\n". Thus the distinction here is a matter of what you call it, not how it is treated.
That is the same as a form of "automatic statement-terminator insertion" where that statement-terminator is whatever you want it to be. And to me, that is as form of "semicolon" (which is being used as a generalization for statement-terminator) insertion.