When I put the mouse cursor on a transparent texel and check the Info panel, there is only the Alpha value displayed, but empty for RGB:
Using a term
texel doesn't make much sense in Photoshop: it's pixels. Photoshop doesn't keep color information for transparent pixels: a pixel needs to be at least 1/256 non-transparent to have any color information.
Sometimes you might see a color in the Info panel even if opacity is 0%: that's only because there's a slightly-non transparent pixel in there and it's transparently less than 0% in 0-100% integer scale (
1/256*100 = 0.39%, Photoshop 'rounds' this to
You are right there is no such thing as a transparent pixel! All pixels have a color even fully transparent ones.
You can get this value, photoshop just uses a lot of energy to keep people thinking transparent is a color of its own. And for some reason 100% transparent is white by default in Photoshop, this makes PS sometimes a bit problematic for game assets. Anybody who interpolates values knows differently*. There are essentially 2 ways, and any combo thereof.
The image calculations is impervious to Photoshop's sleigh of hand. This is useful if you want to decompose the channels as they are and move over to channel based workflow at some point (see below).
Scripting layer has access to the actual data of a pixel
Now there is a lesser known mode in Photoshop, back to 1980's. Does not work well with layers but solves this issue (clunky) with channels. All you see is the opaque values and lapha is taken form channel called alpha. So if you really need to color the transparent pixels do this:
Just copy the red channel over to a new channel, green abd blue also then alpha as separate. Delete layers and make the new channels the R G B channel and copy alpha as a channel named alpha. You will miss all photoshop's functions but you can do this as a last step, or last resort. You can decode this as an action so you only ever have to do this once.
Photoshop essentially is a bad editor for non-image work. A lot of other tools are way better. Anybody who does vfx will has to stand where you are now, at some point.
* One can debate wether this is good or bad. Lets just say this is the way they have chosen to implement this. Its ok if you only ever do images for print, ist semi ok if you only do images for 1:1 size display in digital. It can be problematic, but in 3d and vfx its a severe limitation. It has the benefit of needing a lower amount of brainpower to accept.