Support BYOK models for sub-agents, or disable sub-agent delegation when Copilot quota is exhausted

Title

Support BYOK models for sub-agents, or disable sub-agent delegation when Copilot quota is exhausted

Body

Hi Copilot team,

I'd like to suggest an improvement for the BYOK (Bring Your Own Key) experience.

Currently, I use a custom model through BYOK for almost all of my work. The main agent correctly uses my own API key, so no Copilot model quota is consumed.

However, I've noticed that when Copilot decides to delegate work to sub-agents, those sub-agents still use Copilot-hosted models instead of my configured BYOK model.

This leads to an issue:

My primary agent continues to work through BYOK.
Sub-agents consume Copilot model quota instead of using my BYOK model.
Once my Copilot quota is exhausted, Copilot may still attempt to delegate work to sub-agents, but those tasks fail with a "Limit reached" message because the required Copilot model is no longer available.

From a BYOK user's perspective, this creates an inconsistent experience. Since I'm already providing my own API key and model, I'd expect the entire workflow to use it whenever possible.

I think any of the following approaches would significantly improve the BYOK experience:

Allow sub-agents to use the configured BYOK model.
If the selected BYOK model supports the required capabilities, sub-agents should inherit the same model and API endpoint instead of switching to Copilot-hosted models.
Automatically disable sub-agent delegation when Copilot quota is exhausted.
If sub-agents cannot run because the user's Copilot quota has been reached, Copilot should avoid creating them and instead continue the task with the main BYOK agent, even if execution becomes slower or less parallel.
Provide a user-configurable option for sub-agent model selection.
For example, add settings such as:
Use BYOK model for sub-agents when available
Never use Copilot-hosted models for delegated tasks
Automatically fall back to the main BYOK agent when Copilot-hosted models are unavailable

This would give BYOK users full control over which models are allowed to execute any part of their workflow and avoid unexpected Copilot quota consumption.

I believe this would make the BYOK workflow much more predictable and consistent. Users who choose BYOK generally expect their own configured model to be used throughout the entire agent workflow, rather than only by the primary agent while delegated tasks still depend on Copilot-hosted models.

Thank you for considering this improvement!

---
| Field | Value |
| --- | --- |
| App version | 1.0.23 |
| OS | macOS 13.7.6 |
| Theme | GitHub |
| Path | /chat |
| Tenure | Week 7 |

Start at the /chat flow and trace how BYOK model selection and sub-agent delegation are represented; the issue names no files or tests, so first map those entry points. Done means delegated work respects the configured model or avoids unavailable Copilot models, with behavior covered for exhausted quota.

索引モデルが issue の本文から書いたものです。