is the new dbt clone command supported natively by Dagster's DbtCliResource?

It should be. If you're using

@dbt_assets

then you can do the following:

@dbt_assets(manifest=dbt_manifest_path)
def dbt_clone(context: AssetExecutionContext, dbt_resource: DbtCliResource):
    yield from dbt_resource.cli(["clone"], context=context).stream()