Fortunately:

No support for Core or Supervised—can I still use them?

You can still use them even if we no longer support them. There are many users running Home Assistant in all kinds of unofficial ways. This change just means we are removing it from our end-user documentation and will no longer recommend using these installation methods from an official standpoint.

Will the developer documentation on these things remain?

Yes, those will remain. The developer documentation for running Home Assistant’s Core Python application directly in a Python virtual environment will remain. This is how we develop. This proposal is about removing end-user documentation and support.