I just solved this problem like this (background.png and colorWithAlpha.png have the same dimensions):
Bitmap bg = new Bitmap("background.png");
Bitmap overlay = new Bitmap("colorWithAlpha.png");
float m = 0;
Color c;
for (int i = 0; i < bg.Width; i++)
{
for (int j = 0; j < bg.Height; j++)
{
m = overlay.GetPixel(i, j).A / 255f;
c = HSVtoRGB(overlay.GetPixel(i,j).GetHue(), overlay.GetPixel(i,j).GetSaturation(), bg.GetPixel(i, j).GetBrightness());
c = Color.FromArgb((int)(m * c.R + (1 - m) * bg.GetPixel(i, j).R), (int)(m * c.G + (1 - m) * bg.GetPixel(i, j).G), (int)(m * c.B + (1 - m) * bg.GetPixel(i, j).B));
bg.SetPixel(i, j, c);
}
}
public static Color HSVtoRGB(float hue, float saturation, float value)
{
// HSV contains values scaled as in the color wheel:
// that is, all from 0 to 255.
// for ( this code to work, HSV.Hue needs
// to be scaled from 0 to 360 (it//s the angle of the selected
// point within the circle). HSV.Saturation and HSV.value must be
// scaled to be between 0 and 1.
double h;
double s;
double v;
double r = 0;
double g = 0;
double b = 0;
// Scale Hue to be between 0 and 360. Saturation
// and value scale to be between 0 and 1.
h = ((double)hue / 255 * 360) % 360;
s = (double)saturation / 255;
v = (double)value / 255;
if (s == 0)
{
// If s is 0, all colors are the same.
// This is some flavor of gray.
r = v;
g = v;
b = v;
}
else
{
double p;
double q;
double t;
double fractionalSector;
int sectorNumber;
double sectorPos;
// The color wheel consists of 6 sectors.
// Figure out which sector you//re in.
sectorPos = h / 60;
sectorNumber = (int)(Math.Floor(sectorPos));
// get the fractional part of the sector.
// That is, how many degrees into the sector
// are you?
fractionalSector = sectorPos - sectorNumber;
// Calculate values for the three axes
// of the color.
p = v * (1 - s);
q = v * (1 - (s * fractionalSector));
t = v * (1 - (s * (1 - fractionalSector)));
// Assign the fractional colors to r, g, and b
// based on the sector the angle is in.
switch (sectorNumber)
{
case 0:
r = v;
g = t;
b = p;
break;
case 1:
r = q;
g = v;
b = p;
break;
case 2:
r = p;
g = v;
b = t;
break;
case 3:
r = p;
g = q;
b = v;
break;
case 4:
r = t;
g = p;
b = v;
break;
case 5:
r = v;
g = p;
b = q;
break;
}
}
// return an RGB structure, with values scaled
// to be between 0 and 255.
return Color.FromArgb((int)(r * 255), (int)(g * 255), (int)(b * 255));
}
The function HSVtoRGB is taken from https://bytes.com/topic/c-sharp/answers/236124-how-would-i-change-hue-bitmap, slightly adjusted as the original function expects all inputs as values from 0-255, so the scaling has to be removed.