Get task buttons working for Claude

[TylerLeonhardt]

By hard coding it along with CLI...

[Copilot]

Pull request overview

This PR extends “background/local workspace agent” behavior (notably task/terminal affordances) to Claude Code sessions in the Agents (Sessions) window by treating Claude Code similarly to Copilot CLI sessions.

Changes:

• Added a shared helper to identify workspace-backed agent session types (currently Copilot CLI + Claude Code).
• Updated active-session context key wiring and terminal path resolution to use the shared helper.
• Expanded terminal contribution test coverage to include Claude sessions and repository-only archival cleanup.

Show a summary per file

File	Description
src/vs/sessions/services/sessions/common/session.ts	Adds isLocalAgentSessionType helper for Copilot CLI + Claude Code session-type checks.
src/vs/sessions/services/sessions/browser/sessionsManagementService.ts	Uses the new helper to drive the “background provider” active-session context key.
src/vs/sessions/contrib/terminal/browser/sessionsTerminalContribution.ts	Uses the helper to decide when to use worktree/repo cwd and when to close terminals on archive/remove.
src/vs/sessions/contrib/terminal/test/browser/sessionsTerminalContribution.test.ts	Adds Claude-specific terminal cwd tests and a repository-only archived-session terminal close test.

Copilot's findings

Comments suppressed due to low confidence (1)

src/vs/sessions/contrib/terminal/browser/sessionsTerminalContribution.ts:160

• The comment says this closes terminals for a session’s “worktree”, but getSessionTerminalInfo now uses worktree or repository (and unwraps agent-host URIs). Update the comment to match the behavior so it’s clear terminals can also be keyed/closed by repository path when no worktree is present.

		// When a session is archived or removed, close all terminals for its worktree
		this._register(this._sessionsManagementService.onDidChangeSessions(e => {
			for (const session of [...e.removed, ...e.changed.filter(s => s.isArchived.get())]) {
				const info = getSessionTerminalInfo(session);
				if (info) {
					this._closeTerminalsForPath(info.cwd.fsPath);

• Files reviewed: 4/4 changed files
• Comments generated: 3

[TylerLeonhardt]

Addressed: renamed isLocalAgentSessionType → isWorkspaceAgentSessionType, updated JSDoc and comments to describe workspace/worktree-backed behavior rather than locality. Renamed the backing field _isBackgroundProvider → _isWorkspaceAgent to align semantics.