I copy paste here the IRC discussion and test we had with @raghukamath today:
[10:34] <deevad> Ok, tested. A bit of a deception, I was probably too teased by this new mode.
[10:35] <deevad> The shading part (in gamme 2.2) is equal to Hard Light, to the pixel
[10:35] <deevad> while the lighting part is more over exposed
[10:36] <deevad> comparation: (the bright highlight is lambert)

[10:36] <deevad> Hard Light can do this over exposed light by the way
[10:37] <deevad> It simply mean Lambert burn the color to white more quickly, and so allows a less subtle shading work
[10:37] <deevad> Maybe the (Linear) version brings something new
[10:37] <deevad> but I don’t work in Linear color space
[10:37] <raghukamath> deevad: very quick to test thanks.
[10:38] <deevad> I can’t tell
[10:38] <raghukamath> I think the subtle difference from hard light can be handled with opacity, color tone in hard light?
[10:39] <deevad> raghukamath: sure, you can always use grayer colors to get less out-of-the-top bright highlight burst, but on a 0 to 255 scale, that just reduce your options
[10:39] <dmitryK|quack> deevad: the idea is that for gamma2.2, the neutral color if 0.5, and for linear neutral color is 0.215
[10:41] <deevad> dmitryK|quack: Maybe this new mode is more adressed to 3D artist who wants to do compositing in Krita, PBR style?
[10:42] <deevad> and output from Blender their local color, and shading pass?
[10:42] <dmitryK|quack> we need to ask _despair for that I’m afraid
[10:42] <deevad> ok
[10:42] <deevad> I’ll report my notes on K-A and ask at the same time.
[10:43] <raghukamath> the modes are in hsy section right
[10:43] <raghukamath> deevad: can you also share the appimage in your post
[10:45] <deevad> raghukamath: I’ll do, good idea
[10:45] <raghukamath> i see lambert in hsy
[10:45] <raghukamath> there are two right
[10:45] <raghukamath> are there any other extra modes?
[10:45] <deevad> yes , two variation, 2.2 and Linear.
[10:46] <dmitryK|quack> raghukamath, deevad: I’ve checked the maths, yes, when the source color is below 0.5, then maths of Hard Light and “Lambert Lighting Gamma 2.2” is exactly the same. Though when the source is greater than 0.5, the maths is a bit different: Hard Light clips the highlights in a per-channel manner, which can theoretically change the hue of the color, and Lambert does the clipping in HSY color space, which can, in theory avoid hue drifts
[10:46] <dmitryK|quack> can you look closely for the hue drifts when adding very bright highlights?
[10:47] <dmitryK|quack> that should be the main difference
[10:47] <deevad> dmitryK|quack: Ha, thanks for checking that part. Indeed. It can be a huge difference. I’ll test again
[10:47] <dmitryK|quack> (you might also need to test it on an image with vivid colors)
[10:47] <deevad> ok 
[10:51] <raghukamath> yes it seems to preserve hue better than hard light
[10:51] <raghukamath> hard light has preservation of the light and dark and less mid range hues
[10:52] <raghukamath> Imgur: The magic of the Internet here check it
[10:53] <raghukamath> I am lowering the lightness of the base orange hardlight doesn’t vary that much in terms of the white highlight
[10:53] <deevad> Yes, same observation. Too bad Lambert-gamma sort of over expose to white quickly.
[10:54] <raghukamath> is lambert linear for linear colour space
[10:54] <deevad> on a 0 - 255 scale, I easily loose 25% of the brightness subtle work; it’s like being constrained to shade with 0 - ~190
[10:54] <raghukamath> yes
[10:54] <raghukamath> the birghter details are preserved well in hard light
[10:54] <raghukamath> sacrificing the hue mid range though
[10:55] <raghukamath> in this the brighter details are washed out preserving the hue and mid range
[10:55] <deevad> raghukamath: no, I speak about the 2.2. (and yes, Linear is obviously like that, I understand Linear Gamma, good for 16bit workflow I guess)
[10:55] <raghukamath> yes I understood
[10:55] <deevad> 
[10:55] <raghukamath> in the gamma the highlight has too less details
[10:55] <deevad> yes
[10:56] <raghukamath> I think it is somewhat similar to hard light deifference being it preserves mid ranges better than hard light. and it can be useful in some instances
[10:56] <deevad> but that’s probably hard to avoid with how light works. This thing goes additive very quickly. Too quickly
[10:56] <deevad> raghukamath: Yes, same conclusion.
[10:57] <raghukamath> in this you can also see that darker side is almost exactly sam
[10:57] <raghukamath> so it is hardlight with over exposed lighter side giving us more mid range when base layer has darker colour
[10:58] <deevad> Yes
[10:58] <deevad> It makes me wants to go 16bit only to avoid banding issue with using this mid-ranges
[10:59] <deevad> (and 16bit gamma corrected, not even linear xD)
[10:59] <raghukamath> I would probably use it to enhance contrast and a bit of hue in dark artworks which has less highlights but I think those type of artworks are less in my work
[10:59] <deevad> Sure, it sounds like a reliable blending mode for vignette and global highlight/glow
[10:59] <raghukamath> I would need to paint the highlight parts over this
[11:00] <raghukamath> this would kill the details in those areas
[11:00] <deevad> it somehow feels like the Luminosity SAi tool on the light side
[11:01] <deevad> Should we copy/paste the IRC log to DespAir on K-A raghukamath ?
[11:02] <raghukamath> sure
[11:02] <deevad> ok, I’ll do, thanks