I know the small pot you mentioned. To tell you the truth, that small pot can only be used for decoration, and it can't be used at all. The lid is on Taobao. You can have a look at local sellers in Chengdu, but I advise you not to buy it, because buying it is a waste. This pot is so thin that it can be burnt with a very small fire, and it doesn't need an induction cooker. It's like chicken ribs anyway.
The pot for baking egg cakes is the kind of copper pot, because it is thick enough to make. Also, the microwave cake powder sold outside is useless and expensive, so it is better to use ordinary flour. If you really want to make an omelette at home, it is recommended to use a general non-stick pan, scoop a spoonful of batter with a small spoon, make it into a small circle, and then add stuffing.