Ahhh! Eugénie, I was about to ask you if you knew anything about my wee ringholder and then you posted one in green that looks very like it!
Mine is also 5.5cm in diameter, it's 6cm tall, and has no markings at all.
Given the size of it, and of your pots with it, I wonder if this was a "toy" set for a girl?
I haven't seen the pattern on your pots anywhere else before either.