When a CLI agent is invoked from VSCode Copilot Chat, current agent selection is not honoured and most tools are not available

### Describe the bug

Version: 1.113.0-insider
Commit: 145c1854e758de327fc307453ee05e3d46edd9b9
Date: 2026-03-18T15:54:11+11:00
Electron: 39.8.2
ElectronBuildId: 13563792
Chromium: 142.0.7444.265
Node.js: 22.22.1
V8: 14.2.231.22-electron.0
OS: Darwin arm64 24.6.0

GitHub Copilot CLI 1.0.9.

Whenever I use Copilot Chat to send a prompt to CLI (via agent handoff dropdown), CLI *often* is not able to address my requests due to wrong agent invoked, and results in response:
`I’m blocked by this session’s toolset: I only have skill-loading/intent tools, not file read/edit/test/browser execution tools. So I can’t safely implement or verify the three homepage tweaks from here.`

List of available agents below, sample scenarios:
- Select frontend agent in CLI
- Select same agent in Chat
- Send a prompt
- > get result as stated above
----
- Restart CLI
- Leave default agent (i.e. none of my custom ones)
- Select Frontend agent in chat
- > Same 'not able to address' response

---
- Ask what agent are you?
- I am Atlas..
EOF.
---

My thoughts:
While Atlas is an orchestrator, it still should be able to call subagents (and it works as expected when I use CLI directly), but what's weirder is that I never selected Atlas in any of the scenarios above. I used it for previous session, it worked fine, but then I needed some targeted fixes and was not able to do this from VSCode Chat -> CLI handoff because Atlas seem to be invoked for any prompt now even when I am not asking for it.

### Affected version

_No response_

### Steps to reproduce the behavior

_No response_

### Expected behavior

_No response_

### Additional context

_No response_