It only seems that way, for the colors, because the old sprites had pillow shading and like 4 shades jumbled into one scene, whereas the new sprites only have a highlight and a single shade. The star tip, I derped on myself.
I've worked out a system as I refined my process, that I noticed helped, as I practiced more in my toonwork. I do the hue-shifting more aggressively on the characters, so that they stand out much more from the background, and give them black outlines (but not 0, 0, 0 black; no color ever gets below 8, 8, 8 ). For the BG, I do it less aggressively, but still enough to be noticeable, so that the BG isn't dull looking, but also not as vibrant as the characters.
Shifting to blue or purple is actually for the 3rd or 4th shades (for colors that allow it to be) of colors that otherwise wouldn't get there right away. For example, yellow. First, yellow shifts to red. From there, it starts to get more bluish-purple with the 3rd and 4th shades. For grays, reds and blues, Purple is pretty much the straight forward path, since green already has so little bearing over what the color result is.
For highlights, it also depends on the color. Nothing ever goes to yellow straight away, unless it's already within that vicinity, like reds and oranges. Grays and purples go towards blue, and then towards green, and then towards yellow, for the respective shade levels.
Now, if there was a palette system in the development tool, I could have the sprite palettes directly updated to have the shades reflect what type of light they're in (like if there's a blue moon, all the colors would change slightly to reflect that). Since there isn't, instead what I'd use is an overlay for the area (basically whatever the flat color of the blue moon is, for instance, drawn over the screen (but under the GUI) at an alpha, so that everything has that effect). Because of this, I keep all the shading in the general shifting rules as mentioned in the first two sections above, so that I can use an overlay, and not have to make a billion sprite sheets for each specific lighting scenario.
I could experiment with shifting to the respective colors for BGs even less aggressively than I already do compared to sprites, but I'm not sure if it'll actually look better, rather than making the BG look duller and less colorful.
EDIT
So I tried the less aggressive shifting on the tiles, but did my usual go-to shifts.
Old vs New