How much does a Gilded Key cost?

If you can, buy before the run. The shop price of 100,000 is the lower of the two, and the black market vendors inside an Egg Heist charge 150,000.

You find Gilded Keys in the shop under the Equip section. The usual advice is to carry one or two into every Egg Heist run, so plan to buy them in the shop rather than paying the higher vendor price once you're already inside.

The keys earn their price in the locked rooms. Those rooms always hold chests, with loot set by the room's rarity, and they can hold eggs, rare chests and egg nests too. In a Chaos run almost no eggs are left in the open, which means the locked key rooms are close to the only place you'll find one. The other key types and the doors they open are covered in the linked keys article.

Not settled: The Gilded Key has no single settled price. It costs 100,000 in the shop before a run and 150,000 from black market vendors inside an Egg Heist. The game hasn't made clear whether that is a deliberate markup inside the run or whether the price has changed.