[client] Store the account email after a GUI SSO login

The daemon returns the authenticated user's email from WaitSSOLogin but
cannot persist it: it runs as root while the per-profile state file is
user-owned. The CLI's handleSSOLogin writes it after its own WaitSSOLogin;
the GUI path read the value and dropped it.

The profile was therefore left with no email, so Profiles.List showed no
account for it, and later logins and session extends went out with no
login_hint — leaving the IdP to pick an account instead of reusing the one
the profile belongs to. Mirror the CLI and store it, next to the Logout
path that already clears the same file for the same reason.

client/ui/services/connection.go

@@ -242,6 +242,22 @@ func (s *Connection) waitSSOLogin(ctx context.Context, p WaitSSOParams) (string,
 		return "", s.classifyDaemonError(err)
 	}
 	log.Infof("SSO login completed, daemon reported success")
+
+	// Persist the account email the same way the CLI does after its own
+	// WaitSSOLogin: the daemon returns it but cannot store it, since it runs as
+	// root and the per-profile state file is user-owned (see Logout below).
+	// Without this the profile has no email, so Profiles.List shows no account
+	// and later logins and session extends go out without a login_hint —
+	// leaving the IdP to guess which account was meant.
+	if email := resp.GetEmail(); email != "" {
+		if err := profilemanager.NewProfileManager().SetActiveProfileState(&profilemanager.ProfileState{
+			Email: email,
+		}); err != nil {
+			// Non-fatal: the login itself succeeded.
+			log.Warnf("failed to store account email for the active profile: %v", err)
+		}
+	}
+
 	return resp.GetEmail(), nil
 }