No, I didn't have one with me. Even with a Max Hauri mains plug adapter (type E+F (CEE 7/7)), the part is still a lot cheaper than the CH version.

My K5 came with an adapter. Otherwise Galaxus would have delivered it later.

No, unfortunately not! It is not declared as such anywhere. Without Sgrom, even a Kärcher is useless. I was incredibly annoyed.