The lines enclosing the map pin (including my untagged line, sorry) is a park.
I can’t find how to treat these as a single amenity=park - the boundaries are lots of little bits of boundaries of other polygons or bits of fences.
Is it possible to call this area a park without drawing another object? Or do I put a polygon over the existing boundaries of the park and not worry that there are lines on lines?
You can do both. With a type=multipolygon relation you can use existing ways, but the easier - and maybe better - solution is to draw a new way, maybe reusing the existing nodes where feasable. Don’t connect areas with highways, but it is a good idea to reuse the nodes of a fence.