Thanks Jakub, the dual axis solution works great. Just some minor problems:
TLDR: Series from both axis are displayed in the shared tooltip and there is a gap between both axis.
More details:
Troubles arise when the x values are strings, the axis types are category and the shared tooltip is enabled. E.g.
https://jsfiddle.net/q870h2ub/ shows that the two axis seem to be connected, whenever you hover over one series the tooltip shows also the other series from the other axis. We realised that this starts working when we use numeric x values for the points and let them explicitly count up and not intersect for both series. So, presumably the numeric xAxis values of the points which are inferred from the string as the docs say, are somehow "connecting" the two axis here? Do you have any better ideas to keep using this workaround with string x values like in our case?
And another interesting thing - we wanted to get rid of the padding between the axis and apparently this only works when the axis type is not category. See
https://jsfiddle.net/q870h2ub/ vs
https://jsfiddle.net/nzrkuwah/ . Any idea what the reason for that might be?