There are several ways to own an item, but to not have it in your Hoard or Vault. While some steps have already been made to make it clearer when you already own an item, there's a few places where improvements could be made.
Marketplace
The Marketplace (both Treasure and Gem) has the best current support, with an icon to show an item is in your Hoard/Vault, an icon to show an item is applied to a dragon (familiars/apparel/scenes), and an icon to show an item is applied to your account (vistas). It is also possible to filter based on an item being in your Hoard and/or Vault.
It would be nice to also have the ability to also filter items based on whether it is applied to your dragons or account. This makes it easier to for example focus on apparel or familiars you do not already have, instead of having to go through the list of equipped items to find the actual non-owned things.
Grand Exchange
The various Grand Exchange stalls currently only have an icon to show an item is in your Hoard/Vault, but no option to filter out these items. Furthermore, the moment you apply an item to a dragon/your account, this icon disappears, making it impossible to quickly distinguish between items you have never bought and items that are applied to dragons/accounts.
A way to improve this would be to use the same solution as in the Marketplace, which is to add a second icon to the item listing, showing an item is equipped or applied. Additionally, the option to filter out items you already have would be great, especially as stalls get more and more inventory.
Baldwin's Bubbling Brew
Baldwin currently has no way to distinguish items you own from items you don't. It would be nice if Baldwin's recipes, too, could get some icons as described earlier, as well as more filter options.
Swipp's Swap Stand
Swipp also has no way to indicate you already own an item, be that in your Hoard/Vault or otherwise. It would be nice to have an icon to indicate that. Filtering is not necessary here, due to the small volume of trades Swipp has open at any given time.
Wishful thinking: Auction House
Like Baldwin, the Auction House has no icons for items you own, nor filtering options. Unlike Baldwin (and the other shops), the Auction House is highly dynamic, with literal thousands of active listings, which I can imagine makes it infeasible to check whether a player already owns the items listed, as well as to filter on that. It would still be nice to have those options, although it would in my eyes be the lowest priority. I mostly added the Auction House to the list for completeness' sake.
Marketplace
The Marketplace (both Treasure and Gem) has the best current support, with an icon to show an item is in your Hoard/Vault, an icon to show an item is applied to a dragon (familiars/apparel/scenes), and an icon to show an item is applied to your account (vistas). It is also possible to filter based on an item being in your Hoard and/or Vault.
It would be nice to also have the ability to also filter items based on whether it is applied to your dragons or account. This makes it easier to for example focus on apparel or familiars you do not already have, instead of having to go through the list of equipped items to find the actual non-owned things.
Grand Exchange
The various Grand Exchange stalls currently only have an icon to show an item is in your Hoard/Vault, but no option to filter out these items. Furthermore, the moment you apply an item to a dragon/your account, this icon disappears, making it impossible to quickly distinguish between items you have never bought and items that are applied to dragons/accounts.
A way to improve this would be to use the same solution as in the Marketplace, which is to add a second icon to the item listing, showing an item is equipped or applied. Additionally, the option to filter out items you already have would be great, especially as stalls get more and more inventory.
Baldwin's Bubbling Brew
Baldwin currently has no way to distinguish items you own from items you don't. It would be nice if Baldwin's recipes, too, could get some icons as described earlier, as well as more filter options.
Swipp's Swap Stand
Swipp also has no way to indicate you already own an item, be that in your Hoard/Vault or otherwise. It would be nice to have an icon to indicate that. Filtering is not necessary here, due to the small volume of trades Swipp has open at any given time.
Wishful thinking: Auction House
Like Baldwin, the Auction House has no icons for items you own, nor filtering options. Unlike Baldwin (and the other shops), the Auction House is highly dynamic, with literal thousands of active listings, which I can imagine makes it infeasible to check whether a player already owns the items listed, as well as to filter on that. It would still be nice to have those options, although it would in my eyes be the lowest priority. I mostly added the Auction House to the list for completeness' sake.