How parameter serialization should work given this schema:

openapi: 3.1.0
info: 
  title:
  version:
paths:
  /test:
    get: 
      parameters: 
        - in: query
          name: pet
          content:
            application/json: 
              schema: 
                type: string

In case we want specify string value cat for the pet parameter.
Since pet is defined using application/json I expect the serialized url query string to look like this(with quotes percent encoded since the correct json representation for string should be with double quotes "cat"):

https:/example.org/test?pet=%22cat%22

and NOT like this:

https:/example.org/test?pet=cat

Is my assumption correct?

Looking at https://spec.openapis.org/oas/latest.html#parameter-object-examples there is this example which I was looking at which seems logical:

The confusion for me is that swagger editor does not include quotes so it seems like the violation of the spec. And I am building similar UI tool, so I want to better understand how to implement parameter serialization which is one of the most complicated things to do with abnormal amount of edge cases and multiple specs involved.
I created issue on their side: swagger-api/swagger-ui#10661