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What is the purpose of transformers on the output side of a DC power suppply?

I have a PSU that plugs into 220-240V AC mains (L&N, no ground) and outputs 9V DC to a single barrel plug.

On the barrel plug side, just about 10cm before it, there's a little box on the cable that I opened and it reveals a small board with 2 toroidal transformers in series with a 1:1 ratio each. The +9V connects to the primary of the first transformer, directly into the second transformer and then to the +9V lead of the barrel plug. The ground lead is connected analogous to that on the secondaries.

My knowledge is pretty basic I'm afraid. It seems like these transformers are connected in a way that I would think they are two inductors. Okay, that should be an impedance to possible AC but the PSU is rectified and has a cap on the other end already. And why two in series? This is a bit puzzling to me.

So what exactly happens here? Can anyone please clarify?

Thank you!

PS - tips on where to look for how to clean up DC and especially isolate outputs from one another that are derived from one DC output (short of "just use an isolated DC-DC converter") are greatly appreciated.