your question is a bit ambiguous. What is 'Connector Debug output' for you and what is exactly 'inside VSCode' for you, especially under the condition of 'limited access to the machine'?

The connection between VSCode and Cinema 4D to exchange scripts and console output of Cinema 4D is proprietary. It is an websocket connection that runs on the port you define in Cinema (by default 7788), e.g., 127.0.0.1:7788. The payload is JSON but I would rather not publicly document its details, primarily because I do not want to give the impression that there is any guarantee that the protocol is meant to be a stable API third parties can hook into. But since this is a VSCode extension, you can of course just look at the source to understand the details, or ask an agent to do it for you.

When you mean with debug output the actual debugger, then we are using the Microsoft library debugpy. We use port 5678 but you could also use any other port because your app is the server, not the consumer. I.e., the debug IP could be 127.0.0.1:5678. The old (2026.3) docs contained a section that showed how to manually attach from your code to a debugpy client, e.g. VS Code. But I have removed this section in the 2027 Debugging Manual because the debugger is currently not properly working under MacOS and I did not find the time to fix that for 202.0.0 (but I will fix it within 2027.X.X).

Note that the debugger connection is made from your code; your code is the server, VSCode is the client. debugpy is a proprietary Microsoft library and the only meaningful enterprise debugger for Python at the moment. There is the builtin pdb library which you can use but it IMHO has its limits. There are also some smaller third party alternatives, but they are all inconsequential and I do not know if they work with Cinema 4D. debugpy is using the open DAP protocol, so it is not impossible to create your own consumer, but it is probably also not trivial (I am mentioning this because your message somewhat implies that you want to sidestep the VS Code debugger interface).

Cheers,
Ferdinand