Chat turns into a weird disabled state and prevents further input

[bpasero]

Extracted from https://github.com/microsoft/vscode-copilot/issues/17950

Steps to Reproduce:

1. you can test this running out of sources, use a fresh user data dir
2. type "hi" into chat and run through setup
3. uninstall copilot extension and click to restart extension host
4. type "hi" again, extension installs again automatically (ignore the warning output in chat)
5. uninstall copilot extension and click to restart extension host

🐛 things fall apart: the "+" icon shows disabled

You cannot input to chat anymore, there are many errors:

ERR Cannot read properties of undefined (reading 'id'): TypeError: Cannot read properties of undefined (reading 'id')
    at agentAndCommandToKey (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/workbench/contrib/chat/browser/contrib/chatInputEditorContrib.js:34:62)
    at UniqueContainer.value (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/workbench/contrib/chat/browser/contrib/chatInputEditorContrib.js:58:43)
    at Emitter._deliver (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/base/common/event.js:948:22)
    at Emitter._deliverQueue (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/base/common/event.js:959:18)
    at Emitter.fire (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/base/common/event.js:982:18)
    at ChatWidget._acceptInput (vscode-file://vscode-app/Users/bpasero/Development/Microsoft/vscode/out/vs/workbench/contrib/chat/browser/chatWidget.js:1083:40)

[bpasero]

This is caused by #250382 actually because at that point we neither have a core agent nor a contributed agent.