Short answer
Recovery depends on how much chocolate she ingested and how quickly she was treated. The vet likely induced vomiting if it was recent and may give activated charcoal to prevent further absorption of theobromine. They will monitor her heart rate and may run blood tests to check for complications. You'll need to watch her closely at home for at least 24-48 hours for delayed signs like restlessness, vomiting, fast breathing, or tremors. If you see any of these, contact your vet or the ASPCA Animal Poison Control Center at 888-426-4435 immediately.
Hot chocolate — Food safety facts
Do not feed · Cats · full breakdown on the linked food page
Chocolate plus sugar plus milk — the chocolate is the emergency part.
The full verdict, portion guidance and serving notes are collected on the Hot chocolate food facts page.