You have a revolver now.
A revolver and all "gun type" weapons have ammo, like expected. It shows new ammo UI next to the weapon select screen. It just indicates how much ammo you have left. Also, fun fact : you can get a cowboy hat if you have specifically a revolver! But it's a random chance. When you can, you should definitely take it on and off constantly to get this random chance-hat.
You should probably get going. You need to infiltrate, remember?