That's why you're confused. The definition isn't anything to do with what you like, I admire Atget and Evans work greatly, but neither are remembered as SPs. While there were precedents and exceptions, for candid photography the hand held compact 35mm camera was the tool that enabled street photography.
I know how Winogrand did it. He pre-focussed and shot freely, only using the rangefinder if he had the opportunity. A 28mm lens allows you to do that. It's one of the reasons street photographers do not generally use a 50mm lens. People think because they're carrying a Barnack and a 50 like HCB they're street photographers. To get the depth of field and freeze motion with a 50 requires great light and fast film. Most of the time your subjects will be distant, or out of focus or blurred. You're unlikely to get a half body shot and infinity in focus on a 50, something has to give. I'm certainly not claiming candid street photography cannot be done on a 50mm lens, but there's a reason street photographers choose wider focal lengths. Shooting street on an old rangefinder camera means you will be pre-focused much of the time, or you're shooting portraits not candidly.
I absolutely agree. Most current street photography is shot on smart phones.
I'm just looking at it broader. Yes, I like it with people. But it doesn't have to be candid. Atget, Evans and Bresson took plenty of pictures with people aware of their picture been taken.
And even more so in Winogrand's case. Or obviously with Gulden.
To me everything taken on the street with spark of creativity is the street photography. It could be OOF and with blur.
Here are two examples:
http://rangefinder.ru/glr/showgallery.php?ppuser=7332&cat=500
http://rangefinder.ru/glr/showgallery.php?ppuser=2988&cat=500
And I think you are spending to much time on technical accepts, but without practice. On practice, I have missed the focus with 50mm lens on rangefinder camera only few times. Because of focus tab and practice. All what needs to be done is to study DOF calculator, close look at the lens focus scale and learn, get used to positioning of focus tab. With practice it becomes second nature to move focus tab instantly.
And even with RF it takes couple of seconds to focus. With practice.
50mm lens on rangefinder, some are taken with ff2.8. And those are where I don't have much time to focus:
This one is with 50 and f2 taken spontaneously:
This one with 50 and f1.5. Candid is not always about taking it quickly or by "hiding":
The practical reason why we are going wider is only because we want to get closer and still have enough content in the frame. If I walk from less crowded part of the city to the downtown, I could use 50mm lens first and once it is getting crowded, switch to 35mm.
I'm aware what phone is most used camera these days. But I'm not aware of any street photographer who has emerged with it.