I think the problem I am facing is that this filter rule parameter list does not only include shared and project parameters, but also some built-in parameters. As stewart.skyler and caroline.gitonga mentioned, I can loop through all shared parameters of a wall element and retreive only the shared ones.
When there are no shared parameters/project parameters defined, the list looks like this:

If I filter out one wall-type from the project and grab its non-shared parameters, the output looks like this:

You can see, it's not possible to filter for some parameters e.g. the "Coarse Scale Fill Color" parameter. So there are less parameters to filter than there are parameters available on the wall-type.
You can see that some paramters like "Area" and "Length" can not be found in the wall-type because they only make sense on an instanced object.
So if I filter after instances using "WhereElementIsNotElementType()" then the output is the following:

So my question might actually be, what are the rules for the built-in elements to be included into the View Filter Parameter list and is there a way to find out which ones those are?
Thanks 🙂
Edit: the code I used to create the above lists:
List<string> parametersShared = new List<string>();
List<string> parametersNotShared = new List<string>();
FilteredElementCollector col = new FilteredElementCollector(doc).OfCategory(BuiltInCategory.OST_Walls).WhereElementIsNotElementType();
var wall = col.FirstElement();
var wallParams = wall.Parameters;
foreach(Parameter param in wallParams)
{
if (param.IsShared)
{
parametersShared.Add(param.Definition.Name + "\r\n");
}
else
{
parametersNotShared.Add(param.Definition.Name + "\r\n");
}
}
parametersShared.Sort();
parametersNotShared.Sort();