I'm quite often taking things apart to salvage the parts and use them in my projects. Right now I'm taking apart an old PC-power supply for a switch-mode lab-supply project.
The power-supply in question is Delta Electronics DPS-460DB A. Below is a picture of the transformer that I've tried to find info about. Essentially what I'm asking is how in the world does one find basic information on transformers, just like other components? This is not the first time I've pulled my hair out after surfing the "deep-web"(not THE deep-web of course) for info about a transformer and scored absolutely zero. Are almost all transformers custom parts and therefore lack a basic, public, datasheet? What's going on here?
You've got it right. Many (though by no means all) power supply magnetics are custom parts. Your best bet is to try to find the manufacturer of the transformer and see if they list the part on their website. You could also contact them and ask. But odds are a custom magnetics manufacturer won't hand out information about their customers' proprietary designs. This is especially true if the magnetics manufacturer is also the power supply manufacturer.
I'm afraid if you want to understand that transformer, you'll have to take it out and analyze it.