As stated in the title, in Cata Classic you cannot search for items of the type Relic on the auction house. The categories from TBC/Wrath are still present.
This is the case in the default auction house UI and cannot be worked around with something like Aux by inputting the type “Relic” in the search bar.
This can be confirmed in the WoW UI Source file: Blizzard_AuctionUI/Classic
/Blizzard_AuctionData.lua
armorCategory:CreateSubCategoryAndFilter(Enum.ItemClass.Armor, Enum.ItemArmorSubclass.Libram);
armorCategory:CreateSubCategoryAndFilter(Enum.ItemClass.Armor, Enum.ItemArmorSubclass.Idol);
armorCategory:CreateSubCategoryAndFilter(Enum.ItemClass.Armor, Enum.ItemArmorSubclass.Totem);
The Enum.ItemArmorSubclass.Relic is missing from the AuctionData.lua.