Consider using an image that fits the window size perfectly.

scroll_repeat.py

import pygame

pygame.init()

window_size = pygame.Vector2(1920, 1080) * 2/3
screen = pygame.display.set_mode(window_size)

surf = pygame.image.load("image_path").convert_alpha()

surf = pygame.transform.scale_by(surf, 2/3)

running = True
clock = pygame.Clock()

while running:

    dt = clock.tick() / 1000

    screen.fill("black")

    keys = pygame.key.get_pressed()

    if keys[pygame.K_RIGHT] or keys[pygame.K_LEFT] or keys[pygame.K_UP] or keys[pygame.K_DOWN]:
        dx, dy = 0, 0
        if keys[pygame.K_RIGHT]:
            dx += 2
        elif keys[pygame.K_LEFT]:
            dx -= 2
        
        if keys[pygame.K_DOWN]:
            dy += 2
        elif keys[pygame.K_UP]:
            dy -= 2

        """
        w, h = surf.width, surf.height

        a = surf.subsurface(pygame.Rect(0, 0, (w - dx) % w, h)).copy()
        b = surf.subsurface(pygame.Rect((w - dx) % w, 0, dx % w, h)).copy()

        surf.blit(a, (dx % w, 0))
        surf.blit(b, (0, 0))

        c = surf.subsurface(pygame.Rect(0, 0, w, (h - dy) % h)).copy()
        d = surf.subsurface(pygame.Rect(0, (h - dy) % h, w, dy % h)).copy()

        surf.blit(c, (0, dy % h))
        surf.blit(d, (0, 0))

        Into this :
        """
        
        surf.scroll(dx, dy, pygame.SCROLL_REPEAT)

    screen.blit(surf, (0, 0))

    pygame.display.flip()
    pygame.display.set_caption(f"FPS : {round(clock.get_fps(), 2)}")

    for event in pygame.event.get():
        if event.type == pygame.QUIT or (event.type == pygame.KEYDOWN and event.key == pygame.K_ESCAPE):
            pygame.quit()
            running = False