Changing background color by page.draw_rect() when existing white rect

[QQLazy]

Hello,
I want to change the PDF's background color from blank to gray, and I used the method mentioned in PyMuPDF's document：

An efficient way to background-color a PDF page with the old Python paper color is,
col = fitz.utils.getColor("py_color")
page.draw_rect(page.rect, color=col, fill=col, overlay=False)

But I find some pdf have 'white rectangle', after running, the white rectangle still here.Below it's my code, and
the pdf files for testing is attached.

doc = fitz.open('test.pdf')
for page in doc:
page.draw_rect(page.rect, color=fitz.utils.getColor('lightgray'), fill=fitz.utils.getColor('lightgray'), overlay=False, fill_opacity=0.3)
doc.save('test_change.pdf')

However, some pdf softwares can change the background color perfectly which ignore the white rectangle, like this example.

So I wonder if I can use pymupdf to achieve the same effect, the problem bothered me for several days.
Appreciating for your help, thanks.

test_change.pdf
test.pdf

[JorjMcKie]

overlay=False cannot work in this case, because anything "coming later" will of course be "above" it - including white rectangles etc.

[QQLazy]

Thanks for reply, and I know the overlay parameter controls the drawing or text in foreground or background.
But I wonder if there is a way that I can do to deal with the white rect(since I can detect the rect from get_drawings()).
I have thought about two methods:

1. Change the fill color of the rect drawings which is white;
2. Drawing a rect below the text and above the existing rect.

Are the methods I mentioned above can be useful？Or there's another way I can follow.🙏

[JorjMcKie]

No, this is impossible.

[QQLazy]

All right, then I'll let it go, thank you for your help anyway.👌

[QQLazy]

I find that I have made a mistake, the software I thought is useful didn't do anything special, it puts layers in front by default.

So the following code is just the answer I want, if only you let the fill_opacity be small and let overlay=True.

page.draw_rect(page.rect, color=col, fill=col, overlay=False)