In the DDO store > Account > Adventures.
If it tries to sell it to you, you don't own it.
As far as I'm aware, the only exceptions to this are if you bought the below expansions outright instead of via the store for points.
- Menace of the Underdark
- The Shadowfell Conspiracy
- The Mists of Ravenloft
To check if you bought those expansions, they'll be visible in your account information.
https://myaccount.standingstonegames.com/home.php
Cross reference with the list from
https://ddowiki.com/page/Adventure_Pack to determine what you own.
Its not pretty and I too wouldn't mind a more succinct solution, but its what we got. Hope that helps.