Bundles (ex), wherein you dynamically "complete the set", can't be listed on SG at all, since they don't send out information properly, regardless of what is contained within them.

Packages (AKA subs) (which is what this giveaway is listed under) can be detected fine if all that's included in them is base games (as per several Total War collections, for example), it's just the inclusion of even a single DLC that throws them off, since DLC ownership can't be detected by the public API.

However, the user-end API (eg, the one used when you log into Steam Community) is able to access more detailed ownership information, so userscripts can still be used to alert potential entrants if they own a DLC [or DLC-including package] or not).

This works by either syncing SG to your active community log in [for however long you can manage to keep that active before it logs you out, as it's infamously known for doing with excessive eagerness] or by the script performing a sync by request to copy your full DLC ownership information to a local file, which it can then use as a local resource for detecting ownership data on SG (similar to how SG accesses your SG win history to detect DLC ownership for DLCs or DLC-containing packages won through the site).