Electronic – Strange symbol on PSU label

Strictly speaking, it is not a full circuit, but an equivalent full circuit can be easily derived from it, because it has the full information. It has two "labels" (which are not an actual components), which are denoted with the GND symbol (the bottom one) and the triangle symbol (the top one). Both are denoting the voltage levels of the nets they are connected two. The ground is denoting the voltage of 0V (reference potential, to be precise), and the triangle is the denoted (+4V) voltage relative to that reference. The equivalent circuit would look exactly like this one but with a 4V power supply with "+" connected to the triangle, and "-" connected to the GND.

I guess your wall wart is a switching power supply, which can use a high-frequency transformer. In search for a transformer for your own design, you aere looking for a 50/60 Hz transformer, which needs to be much larger and (hence) more expensive.

A transformer roughly works by converting the input electrical energy to magnetic energy, and then converting that to electrical energy again, but at the output voltage. The size of the core of a transformer must be able to contain the magnetic field. At 50/60 Hz this happens 50 or 60 times each second. In a high-frequency switched power supply this happens for instance at 10 kHz (200 times more often than at 50 Hz), so a smaller core can be used to transfer the same amount of power.

I would advise you NOT to try and build your own switching power supply, because your situation requires isolation and a reasonble power, which makes it a specialists project.

As a side note, it is a sad fact of life that the compontes you can find in a mass produced product will together cost much more than the product itself.