I do not think there is a definition of the best way in absolute but rather a mix of internal and external factors that determine the best choice from time to time.
Avoid the hypocrisy of saying that street photography must be stealth so you will not alter the situation: it is often a banal apology to mask the cowardice we have to ask the subject to lay for us.
However, not really a snatched photo is a bad photo.
In this photo I found myself in front of an elderly man who seemed rather dodgy and hostile to be photographed, so I approached as much as I could and I faked a shot elsewhere by pressing my Leica button.
The picture works.
After some months I decided to return there and found the same man in the same place, but this time I was determined, and I was ready to bring home his portrait at any cost. But I had a problem this time: a Leica M rangefinder. Manual focus at f2 on a 35mm lens and brought the camera to eye level.
I did not even think for a second, and decided to bring back the picture, I asked for his permission and with pleasure he turned out to be not only a helpful person, but also a very nice one.
Here too the picture works. Same subject, two different approaches, two very different photographs among them.
I understand that my problem is not asking for permission to shoot, being a confident person, but it is the camera that helped me to a very different kind of photography with the same situation and subject.