The status bar of this window gradually colors in as you scroll down.
"Colors in" is not a standard term among web designers, but English grammar lets you coin a phrasal verb in this way when you need to.
Normally, the subject of "to color in" would be a person applying color to a page, like a child coloring in a picture in a coloring book. I'm suggesting that you make the object that becomes colored the subject of the verb. That might seem strange, but most native speakers wouldn't even notice that it's a neologism unless they were proofreading the sentence. This extension of "colors in" works by analogy with familiar extensions like these:
"These shoes hurt!" "You need to break them in." [That is, you need to wear them for a while to make them become softer and adjust to the contours of your feet.]
(A week later:) "How are the shoes?" "They are breaking in nicely."
"That shirt is pretty baggy on Eddie right now, but he'll fill it out in a year or so."
(A year later:) "Eddie sure is filling out." [That is, gaining weight to match height gained quickly, a common process among growing children.]
"The status bar colors in" is also supported by a weaker analogy with common constructs like this:
That TV show you like is coming on right now.
This is also worth knowing:
Sumer is icumen in. [The name of a Middle English song from the 13th century. This is very obsolete English, but the name of this song is well known and occasionally sung today. It illustrates how old and familiar this kind of construct is in English.]
P.S. I think "fades in" is probably the better answer. But if you're learning English, especially at an advanced level, it's good to know that you have options like "colors in" and how and why this kind of phrasal verb works.
It's also worth noting how "fades in" and "colors in" differ. The primary meaning of "fade" suggests very light, unsaturated colors that result from gradual age or wear, as in "faded blue", "faded jeans". "Fades in" still carries that association, just reversing the process: going from barely visible to clearly visible. "Fades in" would also work with black, white, or grey. "Colors in" is associated with coloring books, and suggests going from black-and-white to colored, without naturally suggesting gradual change (though you can remedy that by adding "gradually", of course). My only reason for doubting whether "fades in" is better is because you mentioned that the status bar might start white rather than transparent.