Shojoshin-in Temple Reservation

I wanted to book a temple stay at Shojoshin-in in November 2024. https://eng-shukubo.net/ linked to https://shojoshinin.jp/, which looks like the official temple website and is accepting reservations.

The website name matches the name of the temple I was searching for; however, everything on the website and in the email confirmation says Seijoshin-in. Is this just a different way of translating the Japanese characters into English?

Has anyone else booked a temple stay using this website (https://shojoshinin.jp/)? I didn't have to put in any credit card info, so I'm not out anything if the booking isn't legitimate, I just don't want to show up in Koyasan and find out that there is no reservation!

https://eng-shukubo.net/reservation/

Your experience differs from what is explained here