Copilot custom agent model caching(?) issue

- Copilot Chat Extension Version: 0.41
- VS Code Version: 1.133.0
- OS Version: Windows 11 Pro
- Feature (e.g. agent/edit/ask mode): agent
- Selected model (e.g. GPT 4.1, Claude 3.7 Sonnet): GPT 5.4
- Logs: I cannot provide as this is on an enterprise account with locked permissions

## Steps to Reproduce:

1. Create at least 2 agents. One as a delegator and another as an arbitrary workload agent that receives subagent delegations. Default the models to GPT 5.6 Sol
2. Load and use them once in the IDE, it will load the correct default model.
3. Edit the default model in an external editor and then check copilot model -- it will still be the old model..

## What we have tried:

When I have the user open the agent.yml in VSCode, add a space to the default model line and erase it, then the default model for the agent properly updates to the one listed in the agent.yml. However, if the user restarts VSCode, it defaults back to the previous agent default and they have to keep re-opening each agent file.

## Side note:

As a side note: These model names/IDs are not posted anywhere in Microsoft documentation for users to utilize. The closest thing is here: https://code.visualstudio.com/docs/agent-customization/custom-agents
But you'll notice that the two examples use contradicting naming standards. The handoff uses "(Copilot)" and the default model doesn't.