Fix "+ New Chat Session" from in-progress cloud agent session

[Copilot]

Clicking "+ New Chat Session" from the agent target dropdown during an in-progress cloud agent session did nothing. The command was invoked with only a position string ('sidebar'/'editor'), so getEditingSessionContext() fell back to lastFocusedWidget—which may not be the chat widget during cloud agent sessions.

Changes

• ISessionTypePickerDelegate: Add optional getSessionResource() method
• chatInputPart.ts: Provide session resource via delegate
• DelegationSessionPickerActionItem: Pass proper IChatViewTitleActionContext when executing ACTION_ID_NEW_CHAT

// Before: widget lookup fails when focus is elsewhere
this.commandService.executeCommand(ACTION_ID_NEW_CHAT, this.chatSessionPosition);

// After: explicit context ensures correct widget resolution
const context: IChatViewTitleActionContext = {
  $mid: MarshalledId.ChatViewContext,
  sessionResource
};
this.commandService.executeCommand(ACTION_ID_NEW_CHAT, context);

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Cannot use + New Chat Session from in-progress session</issue_title>
<issue_description>

Ref https://github.com/microsoft/vscode-internalbacklog/issues/6527

• Kick off a cloud agent session
• Open agent target dropdown
• Select + New Chat Session
• ❓ Nothing happens

</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Cannot use + New Chat Session from in-progress session #289286

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