.tga is supported as-is. Is there a particular .tga file it fails to open?
.webp is the unsupported format I'd most like to add, as that seems to be popular enough nowadays, and it's annoying that it needs to open in a web browser for me. It just seems like a bit of a pain to integrate so I've not jumped on that yet.
I had a quick look into how much work adding animated gifs would be, and it seems very little - almost surprisingly so. I should get that done for the next version, which I'd like to tick-off soon as there's a few other little features/bug-fixes I've done recently.
Regarding opening the default viewer - I'm less keen. I mainly made this to replace Windows' image viewer as the default, rather than supplement it. And for this to be lightweight so an image opens fast and without fuss with a double-click.
I do find I occasionally want to edit an image I have opened (beyond rotating/flipping/etc). And in that case, I'd like to open the image in another program, but not the default program associated with the file format. And presumably I'd like this to work for images pasted from the clipboard, or files that have been rotated/flipped but not saved, which may involve saving to temporary files etc. Altogether, there's just a few necessary steps there that take the feature beyond trivial, towards "the details need some thought."