Sidatt: Just now I received the Tomb Raider Trilogy for free from Epic Games (Yes, it's real!), and the first two games were added to my GOG Galaxy library almost instantly, whereas the Shadow of the Tomb Raider: Definitive Edition didn't add. I decided to add it manually for now while waiting for it to appear, when I realized that the Definitive Edition doesn't even exist in the search engine.
I have the same issue, although I was able to find the Definitive Edition in search when searching all titles.
I tried adding it manually, which does start the launcher, but then when the game starts, it redirects to a web page for signing in and then just hangs the game client, which seems to never receive the sign in information. If I launch the game directly from the Epic launcher, the same launcher opens, but sign in is automatic (without redirects).
So, it would appear the trick is finding out how the Epic store application launches the application (with what parameters and possibly environment variables), to be able to add it in Galaxy. Obviously, it should just show up - it would be good to hear from anyone who doesn't currently have this issue for Shadow of the Tomb Raider definitive edition.