Bread and peanut butter are both relatively large sources of sugar…

Maybe your trouble is the bread. Wholemeal are carbs and carbs are sugar. The sugarless peanut butter should not be causing any sugar crashes.

Caveat. Not a trained specialist here. Just someone who has been trying to sort my issues out and wanting to share.

It doesn't produce a huge amount of glucose, mainly a baseline to keep your brain fed. The rest of your body just starts using different sources for food because it generally doesn't need glucose.

Your body prefers to consume glycogen, which your liver produces from glucose. Most people's livers store enough to go about a day if they aren't participating in strenuous activities.

Also, diabetics are told to eat snacks throughout the day because it can be dangerous for them to eat large meals. Large meals often mean a lot of sugar, and since they either can't produce insulin or are resistant to it, they can't easily signal to their fat cells to store the excess energy