I know a lot of people today recommend using a camera or even a phone to copy photos, because the resolution is high, but it makes no sense to me since a scanner is designed to scan, and has dedicated software to get the most out of it without having to use a special stand to keep the image flat, special lights to assure proper white balance and even lighting, and special techniques to avoid reflections and flare.

I always scan images from film or print to a TIFF file, whether for restoration or just analog to digital conversion.

Just like everything else photographic, there are differences in restoration procedures and outcomes. Most people likely use Photoshop for most restoration work, but doing it well requires skill and a lot of time. I also think most people doing this kind of work use more than one program, and in this day of AI this and AI that, programs like Remini are being used extensively (although I don't know if professionally; I would think not.) The problem is that at this point in the development of machine learning, that type of program only works well for creating artificial faces (although they can be remarkably good in a few cases) and pretty much ignores the rest of the photo. Photoshop's neural restoration filter, mentioned by some here, is still in beta, rarely works well for anything, and crashes Photoshop most of the time. I use it very sparingly.

I have "Ctein's Digital Restoration From Start to Finish," both volumes, and he demonstrates pretty effectively that a good traditional restoration can take a very long time using extensive and esoteric masking techniques, but if you see it through, you can be rewarded with a photo that rivals or even exceeds the quality of the original. Of course. it all starts with a great scan, and that is half the battle.

It sounds like this is not what you're looking for, though.

Remini claims that it is a photo restoration app, but it is a phone app, and after 5 free images, it costs $3.99 per week. That's more than the Photographer's package for Photoshop/Bridge/Camera Raw/Lightroom. It only works well on faces, and will give weirdness to blurred details, hair, backgrounds, clothing, etc. Same with others like FaceApp, Facetune, etc.

It probably depends on the level of restoration you want to do. Personally, I strive for the look of the original and not the sanitized, plastic-looking fakery of the AI face apps.