Yes sprouts do contain protein.
1 cup or 88 grams of sprouts contains 3 grams of protein so if you need to increase your protein intake then eating sprouts daily could help you increase your protein intake.
However sprouts while healthy do not provide all the nutrition that our bodies need to thrive.
Eating sprouts everyday is okay and even eating sprouts for breakfast is okay.
But to get more energy, more vitamins, minerals and nutrition you should eat other foods as well such as apples, bananas, carrots, oranges etc.
As long as you're eating other healthy foods then the sprouts will be okay to eat even daily.