One, somewhat formal, way of saying this is idiolect, which you might think of as combining the idio- from idiosyncratic with the -lect of dialect

There could be several words, depending on whether or not the author's national origin was inadvertently disclosed.

Inadvertent disclosure

Tell

Wikipedia defines a (poker) tell:

A tell in poker is a change in a player's behavior or demeanor that is claimed by some to give clues to that player's assessment of their hand. A player gains an advantage if they observe and understand the meaning of another player's tell, particularly if the tell is unconscious and reliable.

If the written passage were a poker hand, and you consider yourself playing against the writer, then the writer has a tell which reveals some hidden information, such as his bias or national origin.

A character in his book consumed a lot of paracetamol. If he were American, he would have called it Tylenol or acetaminophen. Judging from the author's tell, I don't think he is from the US.

Shibboleth

Here is an EL&U answer that describes Shibboleth. (Props to @Jim for his comment.)

This word comes from the Old Testament. Soldiers from the tribe of Ephraim were trying to cross over the Jordan river, but another tribe, the Gileadites, controlled the river. So to identify the enemy soldiers, the Gileadites had the soldiers of Ephraim say a word they'd probably mispronounce.

They said, "All right, say 'Shibboleth.'" If he said, "Sibboleth," because he could not pronounce the word correctly, they seized him and killed him at the fords of the Jordan. (Judges 12:6, NIV)

The inadvertent disclosure would be a shibboleth, if (say) a British author put British words in an American character's mouth.

An American character in his book calls his phone a "mobile." We call them "cell phones" on this side of the pond. Based on his shibboleth, I'm pretty sure the author is from the UK.

Disclosure ok by the author

(Media) bias

When an author writes a review or an editorial, the author reveals his or her bias.

Here is a brief section from Wikipedia's Media Bias.

Media bias is the bias of journalists and news producers within the mass media in the selection of many events and stories that are reported and how they are covered. The term "media bias" implies a pervasive or widespread bias contravening the standards of journalism, rather than the perspective of an individual journalist or article. The direction and degree of media bias in various countries is widely disputed.

At the moment, there are major conflicts between Israel and Hamas. Based on the editorial board's media bias, they don't represent Hamas.