there is no physical shutter key on the X10III, its a google assistant button (you can patch mce or do other userspace input handling to trigger a camera, but there is no physical focus-half-press button anyway).
it sounds very much like lietuvys is describing the well-document camera1 focus model bug, present only in 10III, that affects both sailfish AND stock sony android, but is not present in camera2 api and thus not a problem in modern (non-sfos) camera apps.
e.g.: https://forum.sailfishos.org/t/camera-refuses-to-take-picture-on-10-iii-focus-hangs