This website has a link to download the FFXIVMarket app, working for Windows 7 and Windows 10. This app works like the combat parser a lot of FFXIV players use, in that it reads the network packets of your FFXIV connection. Instead of combat logs, the FFXIVMarket app reads the auction house message of the price and price history on the ingame market board and updates it to the website for public display. It now also reads your inventory (retainers included) data and makes it accessible for searches.
How to use the app? Download it on the main page and set your data center and server, then press "Start". Once you have the app running, click an item on the market board. Its price and history will be uploaded automatically to the website server, updating that item's data. Since the system has been improved, every item data changes as it's updated individually by someone. Every item has an individual page that shows details the current price, the price history and the recipe cost at the bottom, if said item is craftable. This last feature helps you check the crafting cost of any item instantly.
Square Enix doesn't want you to use third party applications, and this is considered one of them. But since this app does no harm by itself and only shares information already available to the players in a more efficient and distributed matter they likely won't have a problem with it. Still, that's just my belief, so they will let us know eventually if they disagree and I, of course, will listen to what they have to say. Thanks to all the people sending advice and opinions on the Discord channel, I read them all.