Unfortunately, as others have stated, Bungie cannot help you, as they have no control over the licenses. The Microsoft Xbox licensing system is entirely on Microsoft's end; they own the licenses, grant the licenses, store the licenses, etc. If Microsoft says you didn't buy the game, then either Microsoft's systems are messed up, you bought the game on a different account, you didn't actually buy the game digitally but remember that you did, or you were license sharing and just don't remember that you were. If Microsoft says they can't help you, then, sadly, your only option would be to purchase it again if you wish to play Destiny 1. If you were able to install the DLC but the base game is showing as a Trial, then the likeliest scenario is that you purchased (but don't remember getting) a physical purchase of a Destiny product, as the DLCs are digital only, but it would require the disk to play. If Microsoft would manage to lose just one of your licenses, it seems strange that it'd be the base game and not one of the DLCs, and outside of a Microsoft hiccup, the physical box purchase with the DLC cards at the time is the only other way to have all the DLC licenses but not the base game license in a digital form. On the upside, if you did manage to get all the DLCs installed normally because you own their licenses, you should be able to find the Destiny physical disk for sale at any physical retailer that resells used or old games for a considerable discount and that will allow you to play without having to purchase the digital version (which will be either Destiny - The Taken King - Legendary Edition on Xbox 360 or Destiny: The Collection on Xbox One); you'd have to purchase the full bundle as the game is not available all on its own, and Microsoft doesn't usually drop the download price even this long after release.

Unfortunately, Bungie doesn't have access to any game code you entered to gain the license digitally from Microsoft if you entered one, or proof that you own the license. Bungie doesn't give out codes or handle them in any way concerning Destiny 1. Along with that, Bungie's systems and API can only read the licenses owned from Microsoft's system itself, and if Microsoft's system says you don't own it, then that's the same information Bungie has. It's not that there's a slim chance for you with this, sadly; there's no chance. Bungie won't grant you a free copy, even if you somehow managed to have a receipt showing your purchase. You'd need to work with Microsoft to recover that license, so it's entirely in their hands. I understand you feel you didn't license share, but is it possible that someone else (a friend or family member, or maybe even an alternative account you, yourself, have) had an account on your Xbox and owned the game, and that account no longer exists on your console? That's the only other thing that might help you out, but if you cannot think of any, then it's back to dealing with Microsoft or simply purchasing the game again if you wish to play it fully.