CRITICAL: Subagents/new sessions default to "Auto" model using up GH tokens even when using BYOK

I use **BYOK** for all of my Copilot usage. However, even when running a main session with a BYOK model it insists on creating subagents/subsessions with the "Auto" model causing **significant, unintended token costs**. It basically used up my monthly Copilot token budget, and I didn't even realize it... 🫤

There needs to be a setting that controls which model is used for subagents/subsessions. Or let us completely disable GH models in the model providers. It's way too pricey anyways.

Start by tracing how the main session's BYOK model is selected and how subagents or subsessions choose the Auto model. Identify the existing model-provider settings and their coverage; done should be a testable way to control the subagent model or disable GitHub models without unintended token use.

Written by the indexing model from the issue text.