feat(v0.6): ctask agents check + doctor integration

ctask agents check [workspace] validates that a workspace's agent
configuration can be launched without launching it: agent type known,
command resolvable on PATH, launch_dir valid, AGENTS.md present,
CLAUDE.md shim present (WARN only, claude type only). agent.env keys
are displayed informationally, with a WARN line when any key shadows a
ctask-exported CTASK_* var. Returns non-zero when any check FAILs.

ctask doctor includes the same sweep when a workspace context is
resolvable — the most-recently-active workspace via
workspace.MostRecentActive. When no active workspace exists, doctor
shows "Agent check: skipped (no workspace context)" without bumping
the failure counter. runAgentsCheckOnWorkspace is shared between the
standalone command and the doctor integration.

TestCompletionSubcommandViaExecute is made order-independent: cobra's
default completion command captures the root output writer on the first
Execute() in the process, and the new agents-check tests now run an
Execute() earlier in the suite.

cmd/doctor.go

@@ -213,6 +213,11 @@ func runDoctor(cmd *cobra.Command, args []string) error {
 	resolver := config.LoadResolver()
 	checkSettings(resolver, &passed, &failed)
 
+	// Check 11: v0.6 — agent check when a workspace context is resolvable.
+	// Uses the most-recently-active workspace (mirrors `ctask last`); skips
+	// with an INFO line when no active workspace exists anywhere.
+	checkAgentForDoctor(&passed, &failed)
+
 	// Summary
 	fmt.Println()
 	fmt.Printf("%d checks passed, %d failed\n", passed, failed)
@@ -364,6 +369,26 @@ func formatSettingSource(s config.ResolvedSetting) string {
 	return base
 }
 
+// checkAgentForDoctor runs the same validation as `ctask agents check`
+// against the most-recently-active workspace. When no active workspace
+// exists, prints a skip line. FAIL outcomes increment the failed counter
+// (so doctor's overall exit code reflects agent breakage); WARN does not.
+func checkAgentForDoctor(passed, failed *int) {
+	_ = passed // reserved for future symmetry with the other checks
+	fmt.Println()
+	roots := config.SearchRoots()
+	best, err := workspace.MostRecentActive(roots)
+	if err != nil || best == nil {
+		fmt.Println("Agent check:  skipped (no workspace context)")
+		return
+	}
+	if checkErr := runAgentsCheckOnWorkspace(os.Stdout, best); checkErr != nil {
+		// runAgentsCheckOnWorkspace already printed the [FAIL] lines; just
+		// increment the counter so the summary reflects the breakage.
+		*failed++
+	}
+}
+
 // checkTmux reports the three-state tmux check (v0.5.3):
 //   - CTASK_SESSION_MODE != "persistent" -> INFO (direct mode, tmux optional)
 //   - persistent + tmux on PATH + version OK -> two INFO lines