In Lab color system your "Original" and "Target" colors have the same L, but in HSB their brightnesses are different. That's because Lab system is developed to present seen colors and HSB presents voltages in a color production machine (=RGB screen) Of course in HSB there's some attempt to take into the account eye's different sensitivity in different colors, but that's very coarse. It can be enough to make color televisions which at least seem to work, but still separates very poorly seen color and seen brightness when compared to Lab system.
You can set Photoshop's color picker to keep Hue and Brightness constant and give a slider to change the saturation. Slide it and see radical changes in Lab system's L.
As well, if you slide Lab's L, all numbers in HSB vary.
The most non-perceptual thing in HSB is the saturation. It presents how far away from each other are R, G and B in percents of the maximum possible in that brightness. Thus nearly pure white and nearly black can well be 100% saturated. Saturation isn't at all the same as colorfulness, it's in percents "how much there is colorfulness of the maximum possible in RGB at that brightness level"
In Lab system we have no single number for colorfulness. Numbers a and b hold as well hue and colorfulness (=chroma). If you want to keep hue unchanged, but increase chroma, you must multiply a and b with the same number. If you want to change only hue, keep sqrt(a^2+b^2) (that's chroma) same, change the ratio of a and b. You get easily out of RGB gamut colors, those which would need RGB values beyond the range 0...255. Photoshop clips the RGB numbers to 0...255. Fortunately Gamut Warning is possible to switch ON.
Your problem: If you must keep Lab's L, then change only Lab's a and b. Use adjustment mechanism which allows it, do not use a mechanism which works via HSB numbers. If you for some for me unknown reason must do the adjustment by changing HSB numbers, then you must adjust all of them to keep L.