fix(handoff): preserve GT_AGENT across session restarts (#788)

Adds GT_AGENT env var to track agent override when using --agent flag.
Handoff reads and preserves GT_AGENT so non-default agents persist across restarts.

Co-authored-by: joshuavial <git@codewithjv.com>

internal/config/loader_test.go

@@ -2670,3 +2670,63 @@ func TestQuoteForShell(t *testing.T) {
 		})
 	}
 }
+
+func TestBuildStartupCommandWithAgentOverride_SetsGTAgent(t *testing.T) {
+	t.Parallel()
+	townRoot := t.TempDir()
+	rigPath := filepath.Join(townRoot, "testrig")
+
+	// Create necessary config files
+	townSettings := NewTownSettings()
+	if err := SaveTownSettings(TownSettingsPath(townRoot), townSettings); err != nil {
+		t.Fatalf("SaveTownSettings: %v", err)
+	}
+	if err := SaveRigSettings(RigSettingsPath(rigPath), NewRigSettings()); err != nil {
+		t.Fatalf("SaveRigSettings: %v", err)
+	}
+
+	cmd, err := BuildStartupCommandWithAgentOverride(
+		map[string]string{"GT_ROLE": constants.RoleWitness},
+		rigPath,
+		"",
+		"gemini",
+	)
+	if err != nil {
+		t.Fatalf("BuildStartupCommandWithAgentOverride: %v", err)
+	}
+
+	// Should include GT_AGENT=gemini in export so handoff can preserve it
+	if !strings.Contains(cmd, "GT_AGENT=gemini") {
+		t.Errorf("expected GT_AGENT=gemini in command, got: %q", cmd)
+	}
+}
+
+func TestBuildStartupCommandWithAgentOverride_NoGTAgentWhenNoOverride(t *testing.T) {
+	t.Parallel()
+	townRoot := t.TempDir()
+	rigPath := filepath.Join(townRoot, "testrig")
+
+	// Create necessary config files
+	townSettings := NewTownSettings()
+	if err := SaveTownSettings(TownSettingsPath(townRoot), townSettings); err != nil {
+		t.Fatalf("SaveTownSettings: %v", err)
+	}
+	if err := SaveRigSettings(RigSettingsPath(rigPath), NewRigSettings()); err != nil {
+		t.Fatalf("SaveRigSettings: %v", err)
+	}
+
+	cmd, err := BuildStartupCommandWithAgentOverride(
+		map[string]string{"GT_ROLE": constants.RoleWitness},
+		rigPath,
+		"",
+		"", // No override
+	)
+	if err != nil {
+		t.Fatalf("BuildStartupCommandWithAgentOverride: %v", err)
+	}
+
+	// Should NOT include GT_AGENT when no override is used
+	if strings.Contains(cmd, "GT_AGENT=") {
+		t.Errorf("expected no GT_AGENT in command when no override, got: %q", cmd)
+	}
+}