client calling out to private method in KernelManager

[jgeraerts]

_async_is_alive calls out to _async_is_alive in the kernelmanager.

https://github.com/jupyter/jupyter_client/blob/main/jupyter_client/client.py#L415

    async def _async_is_alive(self) -> bool:
        """Is the kernel process still running?"""
        from .manager import KernelManager

        if isinstance(self.parent, KernelManager):
            # This KernelClient was created by a KernelManager,
            # we can ask the parent KernelManager:
            return await self.parent._async_is_alive()
        if self._hb_channel is not None:
            # We don't have access to the KernelManager,
            # so we use the heartbeat.
            return self._hb_channel.is_beating()
        # no heartbeat and not local, we can't tell if it's running,
        # so naively return True
        return True

However when using the GatewayKernelManager from jupyter_server this assertion fails https://github.com/jupyter/jupyter_client/blob/main/jupyter_client/manager.py#L696, while it has overridden the is_alive method

So I think _async_is_alive should be made public and the GatewayKernelManager should also be adapted to override this method.

What are your thoughts?