В папке с .py файлом должны быть 3 изображения размером 800 на 600 пикселей.
Вот сам код:
import pygame

import os

pygame.init()

WIDTH = 800

HEIGHT = 600

WHITE = (255, 255, 255)

BLACK = (0, 0, 0)

screen = pygame.display.set_mode((WIDTH, HEIGHT))

pygame.display.set_caption("Игра")

image_1 = pygame.image.load("image_1.jpg")

image_2 = pygame.image.load("image_2.jpg")

image_3 = pygame.image.load("image_3.jpg")

backgrounds = [image_1, image_2, image_3]

current_background = 0

font = pygame.font.Font(None, 36)

def draw_background():

   screen.fill(WHITE)

   screen.blit(backgrounds[current_background], (0, 0))

   button_rect = pygame.Rect(WIDTH - 200, 20, 180, 50)

   pygame.draw.rect(screen, BLACK, button_rect, 2)

   button_surface = pygame.Surface((180, 50), pygame.SRCALPHA)

   button_surface.fill((255, 255, 255, 100))

   screen.blit(button_surface, (WIDTH - 200, 20))

   text = font.render("Сменить фон", True, BLACK)

   text_rect = text.get_rect(center=button_rect.center)

   screen.blit(text, text_rect)

running = True

while running:

   for event in pygame.event.get():

       if event.type == pygame.QUIT:

           running = False

       elif event.type == pygame.MOUSEBUTTONDOWN:

           if WIDTH - 200 <= event.pos[0] <= WIDTH - 20 and 20 <= event.pos[1] <= 70:

               current_background = (current_background + 1) % len(backgrounds)

   draw_background()

   pygame.display.flip()

pygame.quit()