TGA images support transparency and high quality (no compression artifacts). There is no visual difference between using TGA or PNG. PNG is more convenient for development as it displays in Windows explorer and web browsers / content repositories such as Github.
PNG has better compression (deflate method) than TGA. However if the pk3 is a standard compressed zip (deflate method) there may not be much size benefit to using PNG over TGA.
ioquake3 supports PNG images but the official Quake 3 releases do not. So if you want your mod to be compatible with Quake 3 on Steam etc; you’re stuck using TGA and JPEG.
A mod that replaces all the shader files is a bad idea as it may conflict with other mods. It’s also probably not allowed by the Q3 EULA. I would recommend replacing images with the same formats.
It would be possible to use PNG for development with modified shaders and then use a batch script and some program to convert the PNG images to TGA and JPEG where appropriate for releases. Though that diffidently makes things more complicated.