I do not think that there is one Leica Look. Even among Leica shooters, there is debate and discussion about the differences between modern Leica lenses, and the various older Leica lenses. I, myself, see a Leica Glow, that is characteristic of Leica lenses designed by Walter Mandler, being different from newer Leica lenses designed by Peter Karbe. Some Leica shooters will want all of their lenses to be Mandler-designed. Others will want all of most or their lenses to be Karbe-designed, though there is no definitive list of which lenses were designed by Peter Karbe, himself, other than the ones specifically identified during interviews with this often-modest designer.
As I understand it, the Leica Glow is a result of optical corrections being imperfectly-corrected, at least when shot wide-open. I can assert that my Summilux-M 50mm ASPH (Ashperical) is not perfectly-corrected, when shot wide-open, but does become much better-corrected when stopped-down. This is the lens that lured me into adding the Leica M system, in early 2018. It was designed by Peter Karbe.
Notably, several different vintage 35mm Leica lenses each have their own followings, among devotees, who have driven-up the price of some of the classic, vintage Leica lenses. Cosina, under its Voigtlander brand, markets a Nokton 35mm f/1.4 lens that is regarded as being similar to the pre-Aspheric Leica M 35mm f/1.4 Summilux. Notably, one can choose a Single-Coated (SC) version of the Nokton, in order to get images even closer to those captured by the vintage, pre-Aspheric Summilux, the earliest of which, at least, were totally uncoated. The Multi-Coat (MC) version of the 35mm f/1.4 Nokton is available, for shooters who desire the optically uncorrected aspect of the pre-Aspheric Summilux, but prefer the better flare resistance provided by modern Multi-Coating.
Another vintage Leica lens, desired by some shooters, is the 8-Element Summicron 35mm f/2, which has been replicated by Light Lens Lab, a relatively recent, low-volume manufacturerer, in China. I know much less about this one, than the above-mentioned Nokton 35mm f/1.4, which I have handled, when I met a local shooter, who borrowed my Leica M10, to make sure that his aging eyes could still focus with the rangefinder, before he ordered an M10-R.
One major reason that I believe that the %u201CLeica Look%u201D is largely the result of the lenses, is because I use several Zeiss ZM lenses on Leica M cameras. The Zeiss lenses produce a %u201CZeiss Look,%u201D rather than a %u201CLeica Look.%u201D The film-era Zeiss ZM lenses produce a different look than the much newer Zeiss Distagon 35mm f/1.4 ZM. I was familiar with Nikon F-mount Zeiss ZF.2 lenses, so, an M-mount Zeiss Distagon 35mm ZM lens provided a familiar Zeiss Look.
Having said the above, I will now say that there is something about the different Leica digital sensors, too. The M10 has a color palette that I really do like, requiring no corrections for my wifes skin tones, or the clothing she wears. It is different than that produced by the previous model generation, the M Type 240, which I test-shot, before buying an M10. (I only tested the Type 240 indoors, at one camera store.) One fault of Leica digital M cameras, before the M10, is that they did not block enough IR, which affects the colors. Some shooters may have liked the effect, while others have not. The Leica M8 required a UVIR filters, to prevent blacks from appearing purple, in some conditions. Some Leica shooters using IR-cut filters when using Leica M cameras, up to and including the 240-series.
I am not any kind of expert. My formal training was with Canon equipment, for evidentiary/forensic/crime scene photography. My wife mentored me with Nikon Gear, and I am, thus far, self-taught with Leica M system.
