Eventually we made it , I am not very happy with the final result but this is what we have so far. We introduced an intermediary:

defmodule ComponentRendererBehaviour do
  @callback render_component(atom() | map()) :: Phoenix.LiveView.Component.t()
end

defmodule ComponentRenderer do
  @behaviour ComponentRendererBehaviour
  alias Phoenix.LiveView.Helpers

  @spec render_component(atom() | map()) :: Phoenix.LiveView.Component.t()
  def render_component(assigns) when is_map(assigns) do
    Helpers.live_component(assigns)
  end

  def render_component(component) when is_atom(component) do
    Helpers.live_component(component)
  end
end

which gets used:

  def render_child(assigns) do
    @renderer.render_component(assigns)
  end

  def render(assigns) do
    ~H"""
    <div>
      <label for="select_establishment_id_query" ><%= gettext("Establishment") %></label>
      <.render_child
        module={TypeaheadSelect}
        id="select_establishment_id"
        options= {[]}
        selected= {[]}
        on_select= {:SELECT_ESTABLISHMENT_ID} >
        </.render_child>
    </div>
    """
  end

and the test looks like:

test "render the label and the type ahead to select the establishment id" do
      SubComponentTestHelper.expect_sub_component(%{
        module: TypeaheadSelect,
        id: "select_establishment_id",
        options: [],
        selected: [],
        on_select: :SELECT_ESTABLISHMENT_ID
      })

      {:ok, document} =
        render_component(fn _assigns ->
          assigns = %{}
          ~H"<SelectEstablishmentIdComponent.render {assigns}/>"
        end)
        |> Floki.parse_document()

      # ...checks
      document |> IO.inspect(label: 234)
    end
  end

and we have a helper:

def expect_sub_component(expected_assigns) do
    RagingBullWeb.Components.ComponentRendererMock
    |> expect(:render_component, fn used_assigns ->
      actual_assigns = used_assigns
      |> Map.drop([:__changed__, :inner_block])

      assert actual_assigns == expected_assigns

      %Phoenix.LiveView.Rendered{
        static: ["<#{actual_assigns.module}/>"],
        dynamic: fn _track_changes? -> [] end
      }
    end)
  end

This is the very first attempt, so I expect to be able to improve it.