I'm using MySQL 8.0.27.
MATCH (column) AGAINST ('その猫' IN BOOLEAN MODE)
MATCH (column) AGAINST ('"その猫"' IN BOOLEAN MODE)
Both statements show "その小さな猫" in the results.
The documentation says:
For boolean mode search, the search term is converted to a search phrase.
So I would expect to not need the quoation marks, but it does not work in either case.