Are there 2D-Transformers?
They are called &quot;Planar transformers&quot; and they are used in the Telecom industry.
https://www.electronicproducts.com/wp-content/uploads/passive-components-magnetics-inductors-transformers-wcjh-1s-jan201618.jpg
They need a multi-layer PCB because the windings are PCB traces. In the following picture you can see the multi-layer structure of the PCB.
I saw, time ago, a planar transformer printed on a 24-layer PCB.
https://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Planar_Transformer.jpg/1024px-Planar_Transformer.jpg
The soft-ferrite core is than manually added by the worker after the PCB gets populated.
Often, they are manufactured and sold as single products. That is, it's very rare that people print planar transformers on the very same PCB of your final product.