If 8.8.8 didn't work, then check DXT1 which has no alpha.
Added 41 seconds ago
Waterfall_13, can you send a screenshot of the alpha channel? Maybe the problem is just with it?
I suspect that the alpha was simply drawn poorly. However, I may be wrong.
How did you create the alpha? Did you select black on the image and then fill it on the alpha channel?
If so, try instead simply copying the original image and pasting it onto the alpha channel. It will become black and white on the alpha channel. Then adjust the brightness to your liking.
Added 10 minutes ago
There is also a possibility that you need to edit not the image export settings, but the xdb file that controls the texture or material. I don't remember exactly, but there seemed to be a function there that controls actions with the alpha channel. And there are different values. Including normal transparency processing or just a hard "visible/not visible". You need to look and compare how these xdb files are configured for different materials and textures.
Secondly, if you add a solid alpha channel, it will be a black square, which is logical.
Thirdly, if you start customizing the alpha channel to suit your needs, you will get what I showed, that is, black edges, which is also quite logical because I cannot perfectly adjust the transparency with the alpha.
Actually, I was saying that I think the problem is that Photoshop might be opening them incorrectly, or I don't know what the problem is.
When opening the original fire00 texture in Paint.NET, nothing is displayed at all.

When opening in Photoshop, I have black edges.

These textures (original) do not have an alpha channel.

At the moment, the best option that can be devised, but which I don't like, is to manually create my own alpha for TF8888, then we see the effect as I showed in the screenshot in the comment above, where it seems to be purple, but the edges are black.

I can't create a beautiful alpha so that all pixels are transparent with the desired intensity, I'm not an artist -_-