I have some .png files with transparent backgrounds sitting on my desktop right now, and there they are shown with a black background. But once I apply them to some web page, the background is indeed transparent. Did you also try to insert your png into a page?

We actually no I didn't try
Just assumed it wasn't working.

XnView works for me regarding the transparency. I have put a file here containing the following:
(a) a .jpg of a snapshot I took in London's Trafalgar Square;
(b) a .png created from (a) in Affinity Photo by selecting and removing the sky, and exporting as PNG;
(c) a .avif file created from (b) using Tools > Batch convert ...
(d) a screen-shot of the convert settings used for (c).

If the transparency shows properly for others, I'm wondering whether the .png files which showed the black background were exported as PNG while Photoshop or Affinity Photo had more than one layer.

Frank

Well that could be it BCS sometimes I can have loads of layers and sometimes I forget to flatten them before saving.

I made a wee test with Frank's avif file. With HTML Editor I just made a page with some background colour and inserted the avif image. I was not able to select it, but had to write in the file name manually. Then I tested the page in Chrome.
Result: The transparency works!

That's encouraging, Inger. I found that your HTML file also works showing the transparency in the Brave browser.

In Firefox Developer Edition I used about:config and found 'image.avif.enabled' and set it to True. Full implementation there has not yet occurred: the image showed, but with a black background instead of the transparency. It will be interesting to see how quickly Firefox fully supports the format.

With at least two browsers now properly reading AVIF files, a long-standing viewer (XnView) both viewing and converting to that format, and the compression being so good, the future looks promising for it.

My thanks to Stonecherub for drawing attention to this.

Frank