Another data point: Originally I had bought the short adapter cable suggested by Lukas:
In the article description you see that the barrel jack is compatible with 2.5 as well as with 2.1 inner diameter. The reform barrel jack has an inner diameter of 2.1 mm and consequently, this usb-c adapter fits but it is very easy to remove and wiggles a bit. It feels like it could fall off any moment and is very easy to pull out.
So now I tried this one:
This adapter comes with 2.5 or with 2.1 mm inner diameter. I bought the variant with 2.1 mm inner diameter and this barrel jack now really fits very nicely into the plug. It’s still easy to plug in and remove but it doesn’t feel anymore like there is any wiggle room. I also like this adapter because it’s not a cable and thus quite a bit smaller and easier to carry around when traveling.
But both adapters do their job perfectly well.