A nit-picky little clarification here: the Sony A7 III is not a DSLR (digital single lens reflex) camera. It is a mirrorless ILC (interchangeable lens camera). Sony makes several models of mirrorless cameras, including the fixed-lens RX10 and RX100 series. The RX10 is what is considered a "bridge" camera, meaning that it has a long zoom lens which is permanently affixed to the camera. The RX100 is a small, almost pocketable, compact camera with again a fixed lens.
Perhaps you might want to check out both the RX10 and the RX100, as they might be satisfactory for you in terms of providing better image quality than the iPhone camera does, while being lighter in weight and also much more portable -- no carrying around a bagful of lenses when using the RX10 M4, as it has a range from 24mm-600mm (35mm equivalent). The smaller RX100 M6 and the new M7 both have a zoom range from 24-200mm (35mm equivalent).
The iPhone has a much smaller sensor than any DSLR or mirrorless ILC, or than the RX100 and RX10 series cameras, which is a key factor in image quality. Both DSLR and ILC cameras provide much more flexibility in the use of settings and controls, which is another important element in photography. One can control settings for aperture, shutter speed, ISO, etc., and can shoot in RAW or jpg formats. Although there are some apps which can provide limited settings controls, this still is not the same as using a full-fledged camera and the results will show it. Smartphones, including the iPhone, are depending more and more on AI technology to produce results, and while this can be useful and at times quite effective it is not the same as a photographer setting up a camera, gazing at a scene and composing it, then pressing the shutter release to get the exact results he or she is envisioning.
Not knocking the iPhone at all -- in fact this past year I have found myself using my iPhone XS more frequently than my other cameras, as, yes, it's usually with me or nearby so that when I see something interesting I can grab it and fire off a couple of shots. The iPhone has brought fun back into photography for many people, and I'm no exception! That said, when I want do something more "serious," I get out the other gear and use it. For concerts I take along the RX100 m6 and get much better results than I would with my iPhone because I have more control over the settings, which is important when dealing with stage lighting. Often when walking around my neighborhood, which features a small lake, I take the RX10 and am able to shoot just about anything from a wide-angle landscape scene to a closeup of a goose or duck doing something interesting. Again I can control the settings, using spot metering many instances or adjusting the aperture or shutter speed to achieve specific results.
Just some things to think about..... Perhaps replace the Sony A7 III and its lens(es) with something smaller and lighter weight which would still give you more impressive results than the iPhone, and also enjoy the new iPhone 11 Pro as well....
