The coordinates are in the file, not in the picture
Location data is not something you can see by looking at an image. It sits in a separate block of the file called EXIF, alongside the camera model and the shutter speed. Anyone who receives the file can read it in seconds, and on most phones it is on by default.
How precise it actually is
A modern phone records latitude and longitude to six decimal places, which resolves to roughly a metre. It often stores altitude too, which on a tall building narrows things down to a floor. This is enough to identify a specific flat, not just a neighbourhood.
The pictures that give away the most
Not holiday photos. The dangerous ones are the ordinary shots taken at home: a pet on the sofa, a delivery that arrived, a whiteboard in a home office, an item being sold second-hand. Those are the ones people post without thinking, and they are all tagged with the same set of coordinates.
Turning it off is not retroactive
Disabling location for the camera app stops new photos being tagged. Every photo already in your library keeps what it was given. If you are about to send an old one, check it rather than assume.