I apologize for this minor problem because it's more of an annoyance than a problem.

So, I have TES Oblivion GOTY Deluxe in my library, BUT, unlike other games, on the store page and on the GOG's homepage, there is no "IN THE LIBRARY" sign on it. Not to mention I keep getting discount offers for that game (because at some point it was on my wishlist).

I've had this happen with a few games, like Shadow Warrior and Fallout 1 and 2. It seems to be rooted in GOG making a new store version with a different ID, for whatever reason they did so.

Also if you own one version on GOG (normal) and there's a "GOTY" edition made later, you often are treated like you don't own everything already. This happens all the time with RPGs that have DLCs.

Annoying quirks of the GOG store they don't seem to be in a hurry to change, sadly.

You redeemed it with a Prime gift, right?
I have the same issue.

Does this have to do with how it manages internal editions of games?

Or is it a specific gift/giveaway issue?

There's only one version of Oblivion on Gog, but some people suggested that this gifted version could be interpreted as different, because it doesn't grant the extra 2 TES freebies.

There are 2 items on GOG:
• Product ID 1242989820 which is the bundle sold in the store.
• Product ID 1458058109 which is the game redeemed through Amazon Prime.

Don't ask me why they made a bundle comprised of a single game (DLC is not separate), but it's not a unique situation.
The store doesn't tally owned items to determine if you essentially own a bundle by owning everything it comprises, so this particular item isn't marked as owned.

Edit: I just remembered before being made free, Arena and Daggerfall were automatically added to accounts with any purchase of a Bethesda game. The aforementioned bundle may exist for that reason.