Short answer
Yes, this is very dangerous. Tomato leaves and stems contain solanine and tomatine, which are toxic to cats. Repeated daily exposure allows these toxins to build up in your cat's system, leading to serious poisoning. Call your vet immediately for advice, and contact the ASPCA Animal Poison Control Center at (888) 426-4435 if you see any signs of vomiting, drooling, or lethargy.
Tomato leaves & stems — Food safety facts
Do not feed · Cats · full breakdown on the linked food page
The fruit is fine, but the leaves and stems contain solanine and tomatine.
The full verdict, portion guidance and serving notes are collected on the Tomato leaves & stems food facts page.