She’s herding your cats. She is a herding dog. All shepherds are herders.
First, she should get calmer after you get her spayed, so do that ASAP.
Second, get a spray bottle fill it with 3/4 full with water and top it up with lemon juice. EVERY time she goes after the cat, spray her (this does not hurt her) with a high-volume high-velocity shot of water by a hard pull on the trigger spray, then take her by the scruff and put her down. She is to stay down until you allow her to get up. If she fights you putting her down, keep holding her down until she goes quiet and lays still. You’re not doing this to hurt her, just asserting your authority which is similar to what a dog would do - except they would use their teeth! You are just using your hands.
Teach her claiming words with objects that belong to you - whether it be shoes, socks, chair, or the cats - the word is “MINE!” You own it, she’ll learn you don’t share these particular objects, especially MY CAT.
You may have to resign yourself that some dogs are always going to be tending towards their strongest instinct. Some dogs, this is a high prey drive. Some dogs, this is a strong herding instinct… and you’ll have to watch carefully and never trust. I suggest you give your cats a quiet room that only they can get to - perhaps put in one of those swinging kitty door in the door of the room where their litter box, food and water are, and keep the big door to the room closed.
Crate your puppy at night and when you, yourself, are getting tired. Also crate her when you are cooking supper, any time you cannot supervise, and while you are eating dinner. Provide her chew toys while in the crate.
Teach your puppy limits to allowable locations in your house. Some places must be learned as being off limits. No exceptions. Our bedroom is off limits to our dogs.
Do you have a treadmill? Once she is over 8 months of age, use the treadmill to exercise her. Train her how to walk, then jog on the treadmill. This way, you can rest and she can work.
Continue with the leadership trend - she does not bound through doorways ahead of you, does not go up and down stairs ahead of you. Behind your heel always.
Try taking her swimming and teaching her to retrieve something. Swimming is excellent excercise and easy on the joints, especially in a growing puppy.
If you cannot find peace and quiet, and must rehome her, try to find someone who uses dogs for herding. Her best life-time situation is to be used for something for which her mind, soul and spirit obviously crave - HERDING! The traits you describe herd-dog breeders crave in their dogs. A Very Strong Herding Instinct.