BMP encoder lost transparency information

[Poker-sang]

if i load this png, and save it into bmp:

var image = Image.Load(path + "avater_default.png");
await image.SaveAsBmpAsync(path + "a.bmp", new BmpEncoder { SupportTransparency = true });
await image.SaveAsPngAsync(path + "a.png");
return;

The bmp one would lose transparency information while the png wouldn't:

bmp:

png:

Is that a bug?