No. The “bath house” is a mikvah.
You are presumably familiar with mikvahs as a gentile through the ritual of baptism. While there are obviously theological doffernces, it’s the same process of submerging in water, and where the Christian practice came from.
That’s how the author phrased it. I presumed it was for ritual bathing and I did not presume that there was any homosexual context to the intent.
New York is denying them permission because the homosexual community would be up in arms that they can’t have their bathhouses, so they built a tunnel between the synagogue and the Mikvah.
That’s how I took what I read what Jews were up to and why they went about this like this.