Both strategies you've been using are spot-on for handling your toddler's big emotions!
Timeouts can be tricky at this age; they work best once kids are a bit older and can reflect on their behavior with some distance. That said, they can still provide a helpful break from the situation, even if it doesn't instantly calm your daughter. It's often after the fact that the lesson sinks in and the cool-down period has the desired effect. So, keep using them but also layer in the strategy of offering choices and acknowledgment too.
You're already on the right track by addressing the feelings behind the behavior. Helping her label and understand those emotions goes a long way toward managing them. "I see you're so frustrated because your toy isn't working like you want. That's tough! We can try something else with it..."
Beyond that, simple distraction can be effective - toggling between fun distractions and acknowledging feelings. It's all about finding the balance of helping her learn to regulate those big feelings and offering understanding while also ensuring she knows you're in charge.
Great work so far! Toddlers are tricky; their emotions are intense, but your patience and empathy will pay off.