Not all Galaxy S22 Ultra has this issue, but users might face this, particularly in the Snapdragon variant. There is one setting that you need to vary of in case you face the shutter lag on the said device.
There is a toggle switch for tracking AF in Samsung’s default camera app. That feature actually tracks the object on which the camera has been focused. That can deal with a bit of camera lag. Turning it off will remove the shutter lag, with compromise on the AF tracking.
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