How to append the filenames of randomly selected images used in creating a single image to a csv file?

Thank you massively to Paul M who posted the following code in response to my first query on how to compile a "stack" of randomly selected images into a unique image:

from pathlib import Path
from random import choice

layers = [list(Path(directory).glob("*.png")) for directory in ("bigcircle/", "mediumcircle/")]

selected_paths = [choice(paths) for paths in layers]

img = Image.new("RGB", (4961, 4961), color=(0, 220, 15))
for path in selected_paths:
    layer = Image.open(str(path), "r")
    img.paste(layer, (0, 0), layer)

I have the code sat in a for _ in itertools.repeat(None, num): where num defines the number of different images being generated. I end the loop with the following to save each image with a unique (incremental) file name:

i = 0
while os.path.exists("Finished Pieces/image %s.png" % i):
    i += 1
img.save("Finished Pieces/image %s.png" % i,)

So far, so good. The challenge I'm struggling with now is how to append to a data.csv file with the details of each image created.

For example, in loop 1 bigcircle1.png is selected from bigcircle/ folder and mediumcircle6.png from mediumcircle/, loop 2 uses bigcircle3.png and mediumcircle2.png, and so on. At the end of this loop the data.csv file would read:

Filename,bigcircle,mediumcircle
image 0,bigcircle1.png,mediumcircle6.png
image 1,bigcircle3.png,mediumcircle2.png

I've tried the following, which I know wouldn't give the desired result, but which I thought might be a good start for me to run and tweak until right, but it doesn't generate any output (and I am importing numpy as np):

np.savetxt('data.csv', [p for p in zip(img, layer)], delimiter=',', fmt='%s')

If it's not too much of an ask, ideally the first iteration of the loop would create data.csv and store the first record, with the second iteration onwards appending this file.