Since the Vatican City and Rome are interconnected in a way, the tipping culture is indistinguishable. If you were to ask a local, they would say that tipping is not necessary. Americans are more likely to tip than most Europeans, but it’s still a kind gesture to leave the change or tip 5-10% of your bill.
In bars, you can leave your change behind. For cabs, you can tip €1-3 if the ride is fairly short. For restaurants, I usually consider the amount of service and how hard the wait staff has worked for me. If I’ve enjoyed a 4-5 hour dinner and occupied one of their section’s tables all night, I will tip 20-30%, regardless of cultural norms or Roman expectations. Servers are making a liveable wage in Europe, versus Americans, who are typically paid $1-3 per hour.
Don’t feel pressured to tip, but it is always appreciated by Europeans because it is not expected.