TagFilter for GetResources call to get resources that do not have specified tag

In the console, I can go to Tag Editor > Find Resources to Tag. From there I can specify a tag key, and then I can either specify a value or select either "(not tagged)" or "(empty value)".

This page appears to be analogous to the API call GetResources (https://docs.aws.amazon.com/resourcegroupstagging/latest/APIReference/API_GetResources.html). It appears as though I should be able to use this call with a TagFilter to get the same result as on the console page. But I can't find anywhere how to specify "(not tagged)" or "(empty value)"

So in the example python code:

    client = boto3.client('resourcegroupstaggingapi')
    
    response = client.get_resources(
        ResourceTypeFilters=[
            'secretsmanager',
        ],
        TagFilters=[
            {
                'Key': 'my_cool_tag',
                'Values': [
                    'what-to-put-here'
                ]
            },
        ],
    )

How can I format the TagFilters object to return resources that do not have a 'my_cool_tag'?

PS Just to clarify, I want to be able to search across multiple or even all resource types, not just secrets. I think the get_resources call is the right API for this, but I could be mistaken.