Fix cooldown timer visibility after Start; add real-time modal validation; update context.md with prod server

- Cooldown counter now always rendered (hidden) when auto_reply active, shown dynamically via polling
- Modal form validates fields on blur/input with red highlight via .input-invalid class
- Telegram: switched back to tel.4mont.ru proxy (working via /etc/hosts on 192.168.33.19)
- context.md: added prod server 45.129.3.83, deploy commands, NPM routing notes

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

static/styles.css

@@ -1113,6 +1113,11 @@ textarea:focus {
     text-align: center;
 }
 
+.input-invalid {
+    border-color: #dc2626 !important;
+    background: #fff5f5 !important;
+}
+
 @media (max-width: 768px) {
     .login-split { flex-direction: column; }
     .login-promo { padding: 40px 24px; flex: none; }