I made a border in this pong game, but the paddles can cross it. How do I stop that?

PyGame has a feature that does exactly what you want it to do. Use pygame.Rect objects and pygame.Rect.clamp() respectively pygame.Rect.clamp_ip():

Returns a new rectangle that is moved to be completely inside the argument Rect.

With this function, an object can be kept completely in the window. Get the window rectangle with get_rect and clamp the object in the window:

while run:
    # [...]

    key = pygame.key.get_pressed()
    if key[pygame.K_w]:
        paddle1.rect.y += -paddle_speed
    
    # [...]
    
    winRect = win.get_rect()
    paddle1.rect.clamp_ip(winRect)
    paddle2.rect.clamp_ip(winRect)
    paddle3.rect.clamp_ip(winRect)
    paddle4.rect.clamp_ip(winRect)

    # [...]

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