And Monument Valley which has similar game mechanics (you twist the environment around rather than make your way through it).
Regarding the ambiance: no idea :/.
But in the same vein, not on Android there is : Invisible Inc. https://store.steampowered.com/app/243970/Invisible_Inc/ and another game with a little girl and her invisible friend or something and it's turn based and tiled based and there's a back-in-time mechanic. Eh. I am useless.
In a similar vein there is also Hitman Go and Deus Ex Go.
I'm also a fan of Slay the Spire, mostly playing it on PC and Switch. But I triple dipped for the Android version, which has a little bit of clunkiness with the UI but the underlying game is there.