“what is this app called?”
I don’t know whether it is the same one, but mine is Siddur Ashkenaz by OKtm Websites. It also adjusts the siddur depending on the day and appears not to have a Shabat option. (I’ve never tried it on Shabat so I can’t tell for sure!) I use it a lot, most recently at minchah today. The company has a lot of other Jewish apps for Android; I don’t know what they have for Apple.