In 2025.. python 3.12 version, It works effectively.

But your code have problems..
the function should be in lowercase provide_access, run_match
should be like

class Access:
    def __init__(self, user, password):
        self.user = user
        self.password = password


class Run:
    def __init__(self):
        self.passwords = {}

    def add_user(self, user):
        if user.user in self.passwords:
            print("❌ User already exists.")
        else:
            self.passwords[user.user] = user.password
            print(f"✔ User: {user.user}, Password: {user.password} added successfully!")

    def show_pass(self, user):
        if user in self.passwords:
            print(f"✔ User: {user}, Password: {self.passwords[user]}")
        else:
            print("❌ User not found.")


run = Run()

while True:
    print("""
Hi there, You have three options:
1️⃣ Add user
2️⃣ Show password
3️⃣ Exit
""")
    choice = input("Enter your choice: ").strip().title()

    if choice == "1":
        username = input("Enter your username: ").strip().title()
        if username in ["Om", "Vishal"]:
            print(f"{username} is not allowed.")
        else:
            password = input("Enter your password: ").strip()
            access = Access(username, password)
            run.add_user(access)

    elif choice == "2":
        username = input("Enter your username: ").strip().title()
        run.show_pass(username)

    elif choice == "3":
        print("Exiting... Have a good day!")
        break

    else:
        print("❌ Invalid choice.")

I wrote it for you.. more advanced & clean..