MLB.com has a remarkably good glossary that covers topics like minor league options.
https://www.mlb.com/glossary/transactions/minor-league-options
"Once an optioned player has spent at least 20 days in the Minors in a given season, he loses one of his options."
The game OOTP is usually pretty good with details like this, and lists Larnach as coming into the 2024 season with 2 minor league options remaining. But looking at his seasonal game logs, I don't see how he didn't consume more than 1 option during the past few seasons.
The Twins' first game this season was March 28 and Larnach was called back up to the majors on April 16. By my math, that's 19 days, but there could be technicalities as to when a "day" starts. So it is possible that the FO made the move just under the wire and his option this year is preserved (for now).
Sorry, this isn't definitive, but maybe provides a few facts that help the thinking process.