Issue with Tropico 4 Gold Edition Through Backwards Compatibility

Something odd I noticed recently that I'm surprised I haven't been able to find anyone mention. The Gold Edition of Tropico 4 comes with the Modern Times expansion on-disc, which is how I played it on 360. Unfortunately, I've found that when putting the disc into my Series X, it does not entitle me to that content, even though in my experience Backwards Compatibility is usually pretty good about honouring that kind of thing. I even went onto the game's Store page to see if I could just download it, but it was just trying to sell it to me unfortunately.

Anyone have this version of the game and managed to get the DLC to install, or is this just a case of an oversight when setting the game up on Microsoft's end? It's not a particularly expensive piece of content so it isn't a huge deal, but I thought it was worth mentioning.

Is it a single disc or does it have a second one that you install the DLC off of or something?

It's a single disc. You can tell it's different from a normal Tropico 4 disc since it very prominently has "Gold Edition" written on it, but when I put it into my Series X (or presumably a One), it reads it as regular Tropico 4 and just queues only the base game for download.

Honestly, I don't even entirely remember how the install works on 360, I just remember it obviously does since I played that content and unlocked achievements in it on there.