No, you do not need to add parameters with your situation.
You should use URL path list. When using navigation go to page, your data to send would be arbitrary text which will be the path list as it needs to be based on user click of breadcrumb.
Thing about path list is it’s a list, so can have more than one item, such as .com/stores/massachusetts/boston
The above, page name is stores and is item #1 of path list, Massachusetts is item #2 of path list and Boston is item #3
When you use data to send you don’t include page name, only path items after so items from #2. You do not need a / in front of item#2 but do need the / between every path list item after item #2.
When you want to show the breadcrumbs on screen just use get data from url and select path list. This is data source for an RG of type text.