Camera and motion
The camera takes the shots for your 360° photo, and on devices that have one the LiDAR camera measures how far away things are, so the shots line up. The motion sensors let you look around a photo by turning your device.
The shots are stitched on your device. Nothing is uploaded or sent anywhere.
Location
If you allow it, the place where you took a photo and the direction you faced are saved in the photo itself, so you can see where each one was taken. The location is used only while you are taking a photo, and it goes nowhere but into that photo.
If you don't allow it, the app works just the same and your photos carry no location. Keep in mind that a photo you share with its location in it tells whoever gets it where it was taken.
Your photos
Your 360° photos are stored on your device. The developer has no access to them.
Saving to Photos asks only to add to your library, never to read it. A photo you open from Photos or Files is the one you pick, and nothing else in them is looked at.
Nothing else
No analytics, no advertising, no tracking, no third-party services, no account.
Deleting
Deleting a photo in the app removes it from the app. Copies you have saved to Photos or shared stay where you put them. Deleting the app removes everything it stored on the device.