Most of my experience is with third edition where 'Templating' was something I believe you found in the Monster Manual, had Tieflings and their celestial counter parts had a "Planetouched Characters" blurp that told you what abilities you'd gain and your level adjustment as well as a issue of Dragon magazine that incorporated the elemental planes.
I remember having this same crisis when 4e made them a race, I thought I had suffered a Mandela Effect for Dragonborn being in 3rd Edition but I think what I was thinking of were called Half-Dragon, even though they're called Half-Dragon I think it wasn't supposed to be necessarily literal. I had to look that up because I still have a distinct memory of creating a dragonborn character being used as an example of templating in either the MM or the DMG. It could also have been in Dragon magazine, I'll keep looking around until I'm satisfied.
All that said I had to look this up online it's been so long since I had those books handy so take everything I remember with a grain of salt.
Edit: there's also the implied Draconic nature of the Sorcerer class that I'm now remember and could be conflating things.
Thanks for the explanation! Yeah, there's also half-dragons, dragonkin, dragonspawn, dragonborn of Bahamut, draconic creature template... The homebrew I saw was fairly similar to the template. Maybe what you're thinking about were the dragonborn of Bahamut? They were a different type, pre-4e.
I kind of wish they made a variant Dragonborn, a Toril one.
Aand... Not a huge fan of the lineage system from TCoE, but perhaps it could be used to make templates or something akin to them? Would be nice to see templates back, they seemed like a interesting mechanic (if quite complicated, as fitting for 3e).
