Many proper uses of the em-dash put two words visually together—despite being parts of two distinct units separated by the em-dash.

I much prefer using a normal dash with a space on each side - like this.

After all AI didn't pick up these habits out of nowhere - all the tells are good writing advice and professional typography, but used with a frequency you would only see in highly polished texts like marketing copy

On another note, it may be useful to you to know that in most English dialects, referring to a person solely by their nationality (e.g., when you wrote "as a Chinese") is considered rude or uncouth, and it may mark your speech/writing as non-native. It is generally preferable to use nationalities as adjective rather than nouns (e.g., "as a Chinese person"). The two main exceptions are when employing metonymy, such as when referring to a nation's government colloquially (e.g., "the Chinese will attend the upcoming UN summit") or when using the nationality to indicate broad trends among the population of the nation (e.g., "the Chinese sure know how to cook!"). I hope this is considered a helpful interjection rather than an unwelcome one, but if not, I apologize!

https://ysyx.oscc.cc/en/project/intro-past.html

Whether that makes it the "same word" is a philosophical question. But writing "hànzì" is proper when referring to the use of the characters to write Chinese. If one is using it to mean a set of characters (rather than the general concept of characters that come from that writing tradition), they're different sets; and there are typically different expectations for typesetting etc. The decision to produce "CJK Unified Ideographs" in Unicode was not without controversy, and quite a few words have been spent by standards committees on explaining why these characters should share code points while there are completely separate Latin, Greek and Cyrillic scripts (despite shared history and many at-least-seemingly overlapping glyphs).

The word “hanzi” in English is much less commonly used — people studying or discussing Chinese are more likely to call them “Chinese characters” or just “characters”.