How to use if-then-else and loop construct in input transformer in EventBridge?

Is there a way to define if-then-else and looping constructs using JSONPath, while defining the configuring the "input path" for EventBridge Input Transformer?

E.g. For the following input

{
            "category": {
              "name": "Nike Shoes",
              "level": 2,
              "translation": null,
              "ancestors": {
                "edges": [
                  {
                    "node": {
                      "name": "Shoes",
                      "slug": "shoes",
                      "level": 0
                    }
                  },
                  {
                    "node": {
                      "name": "Running Shoes",
                      "slug": "running-shoes",
                      "level": 1
                    }
                  }
                ]
              }
            }
}

I need the output to be

{
    "categories.lvl0": "Shoes",
    "categories.lvl1": "Shoes > Running shoes",
    "categories.lvl2": "Shoes > Running shoes > Nike shoes",
}

The following is the python logic for the output I wish to achieve

if node["category"]["level"] != 0:
    category_hierarchy = list(map(lambda x: x["node"]["name"], node["category"]["ancestors"]["edges"]))
    category_hierarchy.append(new_item["categoryName"])
    for i in range(len(category_hierarchy)):
        new_item[f'categories.lvl{i}'] = " > ".join(category_hierarchy[0:i+1])

if the level of the main category ("Nike shoes" here) is not equal to 0, then I want to loop through its ancestors and define variables of the form categories.lvl(n) with the logic defined in column 2 below, to get the values defined in column 3

Variable	Logic	Value required
category.lvl0	ancestor category with level 0	Shoes
category.lvl1	ancestor category with level 0 > ancestor category with level 1	Shoes> Running shoes
category.lvl2	ancestor category with level 0 > ancestor category with level 1 > main category (with level 0)	Shoes> Running shoes > Nike shoes

I could frame the following JSONPath construct for now, which in plain English, represents:

"if the category level is 0, then proceed to output names of the ancestor categories"

JSONPath - $..edges[?(@.level!=0)]..name Output

[
  "Shoes",
  "Running shoes"
]

However, I am not sure how to proceed further.