According to the PHB, half plate is 750 gp to buy. However, magic items of uncommon rarity cost less. If I was to craft a mithral set of half plate (a magic item), RAW, what amount would I pay?
The amount to buy half-plate is not the amount it costs to craft half plate—the smith needs to sell for more than it costs to make. Crafting half-plate would normally cost (per PHB page 187) half its list price: 375gp.
Your mithral version, at 500gp, therefore costs more to craft.
Also note that, as always, crafting magic items is an optional campaign rule, so check with your DM before investing in this plan, if you haven’t already.
A note on “magic items […] cost”: by default, magic items cannot be bought. It’s easy to skim the DMG and get the impression that they can just be bought, but that’s not what it says, and the price list isn’t guaranteed. If your DM has added buyable magic items to their game, they should also be following the DMG’s advice to consider the table of values listed on DMG page 135 as only suggestions. Mithral half-plate is a great example of an item which should have a higher price than the listed suggestion for uncommon items.