Partial responses (which are not recorded yet) do not display a response ID. The get Response API requires a Response ID. I suppose you are trying to retrieve the partial response using the session ID and hence receiving a 404.
As per my understanding, unless the response is recorded, you cannot retrieve the response and the response ID is not available.

Thank you for your answer! Yeah that is what I figured. It is a little confusing because when you make a response export you are able to get partial responses and they do have a response ID. It is a little odd that you cannot get them as individual responses.

The Response ID in the partial response report is the session ID which changes once the response is recorded. And I agree, this is confusing. :)

Thank you so much for looking into this with me! Yeah I know, in the front-end it is nicely called a session ID. But in the API response-export, the header is called response ID. So I guess partial responses are stored somewhere as an actual response?

Yeah, seems so. Unfortunately, it is not available to us until the partial response is recorded.

Thank you for all your help!