Chat session cannot be routed to chatbot agent using Conversation API updateAgentStatus

I currently implement a chatbot in our help center based on Google’s Dialogflow technology. This works already well, when I put myself as a chat agent into the department I want to use for the chatbot. However, if I remove myself from this department and put any other agent into it, the chat widget stays in offline mode, so that a user cannot start a chat.

Here is the relevant code for this issue.

Help Center:

window.zESettings = {
      webWidget: {
        chat: {
          departments: {
            enabled: ['NI Service Bot']
          }
        },
        contactForm: {
          suppress: true
        },
        helpCenter: {
          suppress: true
        }
      }
  };

Conversation API (Node JS):

if(type === 'updateAgentStatus'){
    graphQlQuery = {
      payload: {
        query: `mutation {
                    updateAgentStatus(status: ONLINE) {
                        node {
                            display_name
                            email
                            id
                            name
                        }
                    }
                }`
      },
      type: "request",
      id: REQUEST_ID.UPDATE_AGENT_STATUS
    };
    logMessage = "[updateAgentStatus] Request sent";
  }
webSocket.send(JSON.stringify(graphQlQuery));
console.log(logMessage);

However, when I log the data coming back, I always see that it uses my account for this graphQL query and not the one from the agent I put into the chatbot department. How can I change this?

I have seen a comment from Bryan here that might indicate that it matters under which Zendesk account the OAuth access token was created:

https://develop.zendesk.com/hc/en-us/community/posts/360051528933

Does this mean I need to log in with the chatbot credentials and generate a new OAuth token then? I was under the impression that an OAuth token is not user-specific and if so, I would expect to see some information in the Chat console about the user who has created the OAuth token.

Thanks for any help pointing me in the right direction!