>>130172224She has the basic spider abilities of enhanced strength, speed, agility, etc.
As Spider-Woman/Arachne what really set her apart was her Psi-Webs. She can create psychokinetic energy webs that act similarly to Spider-Man's webbing. But because she's weaving them with her mind she doesn't have to have physical contact with them, so unlike other Spider-folks she can essentially create them from a distance
After the first Madame Web died, Julia inherited her powers. A psychic connection the the Web of Life and Destiny.
It's this weird pseudo-mystical connective tissue between every world in the multiverse, particularly connecting Spider Totems on every earth.
As the new Madame Web, Julia is now blind but she is also has a number of psychic abilities. She has precognitive abilities that can range from powerful visions of dozens of future events at once that have knocked her into a months long coma. And more immediate flashes of the future that allowed her to fight hand-to-hand with Shang-Chi by predicting his movements. Due to their connection with the Web, her visions usually have to do with Spider Totem heroes
She also now has astral projection and can send warnings or messages to other people, or a full projection of herself.