Using jq to extract multiple json objects

I have been using jq to successfully extract one JSON blob at a time from some relatively large files and write it out to a file of one JSON object per line for further processing. Here is an example of the JSON format:

{
  "date": "2023-07-30",
  "results1":[
    {
      "data": [    
        {"row": [{"key1": "row1", "key2": "row1"}]},
        {"row": [{"key1": "row2", "key2": "row2"}]}
      ]
    },
    {
      "data": [    
        {"row": [{"key1": "row3", "key2": "row3"}]},
        {"row": [{"key1": "row4", "key2": "row4"}]}
      ]
    }
  ],
  "results2":[
    {
      "data": [    
        {"row": [{"key3": "row1", "key4": "row1"}]},
        {"row": [{"key3": "row2", "key4": "row2"}]}
      ]
    },
    {
      "data": [    
        {"row": [{"key3": "row3", "key4": "row3"}]},
        {"row": [{"key3": "row4", "key4": "row4"}]}
      ]
    }
  ]
}

My current approach is to run the following and redirect the stdout to a file:

jq -rc ".results1[]" my_json.json

This works fine, however, it seems like jq reads the entire file into memory in order to extract the chunk I am interested in.

Questions:

1. Does jq read the entire file into memory when I execute the above
   statement?
2. Assuming the answer is yes, is there a way that I can extract results1[] and results2[] on the same call to avoid reading the file twice?

I have used the --stream option but it is very slow. I also read that it sacrifices speed for memory savings, but memory is not an issue at this time so I would prefer to avoid using this option. Basically, what I need is to read in the above json once and output two files in JSON lines format.

Edit: (I changed the input data a bit to show the differences in the output)

Output file 1:

{"data":[{"row":[{"key1":"row1","key2":"row1"}]},{"row":[{"key1":"row2","key2":"row2"}]}]}
{"data":[{"row":[{"key1":"row3","key2":"row3"}]},{"row":[{"key1":"row4","key2":"row4"}]}]}

Output file 2:

{"data":[{"row":[{"key3":"row1","key4":"row1"}]},{"row":[{"key3":"row2","key4":"row2"}]}]}
{"data":[{"row":[{"key3":"row3","key4":"row3"}]},{"row":[{"key3":"row4","key4":"row4"}]}]}

It seems pretty well known that the streaming option is slow. See the discussion here.

My attempt at implementing it followed the answer here.