One of the best gimmicks of our new kitchen was also the second (really small) sink with an extra faucet right next to the cooktop.
Although we don’t have an island, the distance between the main sink and the cooktop is quite large. With the extra pull-out faucet, I can now refill water directly into the pot on any cooking zone. If I need to quickly wash my hands (because I’ve messed around with the food again), the way to washing up is about zero meters. And if I want to quickly pour something off, no one stands between 10 liters of boiling water and the sink. Draining vegetables, canned corn, or similar in a sieve directly in the sink next to the pot it finally has to go into - worth its weight in gold.
By the way, the sink doesn’t take up much space. First, it’s small, and second, it’s so far back that you can still comfortably use a 40x30 board in front of it.
Also good: the sink is flush-mounted. Everything that boils over, spills, and drips can be comfortably wiped into the sink.
Even better: the pull-out faucet can be opened and closed directly at the extended end with one finger. This way, I can perfectly dose the right amount of water on the spot without always needing two hands.